In the comments, Gary Kindel, pointed out, "Just answer the question and stop worrying who is going to use to support a specific dating technique."
So the short answer is yes, radioactivity can and does affect radiometric dating techniques. This is a well established phenomenon and as such, there are many other dating methods that make up for this.
There are a lot of different radiometric dating methods, based on different elements (Uranium Lead, Potassium Argon, Uranium Thorium, Carbon, Chlorine-36, Luminescence, Samarium-neodymium, Rubidium Strontium and more.)
Creationists usually point to carbon dating, carbon 14 decay dating. Carbon dating, like other radiometric dating relies on a fairly constant decay over time. Since the creation of carbon 14 varies slightly due to things like volcano eruptions, a calibration curve can be used to adjust it. Results that use a calibration adjustment are called Calibrated or Cambridge Dates. These dates are usually expressed in regular calender dates. As apposed to Uncalibrated or Libby Dates, that use the BP (before present) date.
Science
Carbon-14 is a radioactive isotope of carbon, with a half-life of
5,730 years,[23][24] which is very short compared with the above
isotopes. In other radiometric dating methods, the heavy parent
isotopes were produced by nucleosynthesis in supernovas, meaning that
any parent isotope with a short half-life should be extinct by now.
Carbon-14, though, is continuously created through collisions of
neutrons generated by cosmic rays with nitrogen in the upper
atmosphere and thus remains at a near-constant level on Earth. The
carbon-14 ends up as a trace component in atmospheric carbon dioxide
(CO2).
An organism acquires carbon during its lifetime. Plants acquire it
through photosynthesis, and animals acquire it from consumption of
plants and other animals. When an organism dies, it ceases to take in
new carbon-14, and the existing isotope decays with a characteristic
half-life (5730 years). The proportion of carbon-14 left when the
remains of the organism are examined provides an indication of the
time elapsed since its death. The carbon-14 dating limit lies around
58,000 to 62,000 years
The rate of creation of carbon-14 appears to be roughly constant, as
cross-checks of carbon-14 dating with other dating methods show it
gives consistent results. However, local eruptions of volcanoes or
other events that give off large amounts of carbon dioxide can reduce
local concentrations of carbon-14 and give inaccurate dates. The
releases of carbon dioxide into the biosphere as a consequence of
industrialization have also depressed the proportion of carbon-14 by a
few percent; conversely, the amount of carbon-14 was increased by
above-ground nuclear bomb tests that were conducted into the early
1960s. Also, an increase in the solar wind or the Earth's magnetic
field above the current value would depress the amount of carbon-14
created in the atmosphere. These effects are corrected for by the
calibration of the radiocarbon dating scale.
http://en.wikipedia.org/wiki/Radiometric_dating#Radiocarbon_dating_method
Nuclear carbon dating is not the only test used to date fossils. There many other dating methods that are used to date things; one of witch is chemical properties of igneous rock formations. Others are thermoluminescence, amino acid, etc.
To answer your question, nuclear weapons testing brought about a reaction that simulated atmospheric production of carbon 14 in unnatural quantities. The huge thermal neutron flux produced by nuclear bombs reacted with nitrogen atoms present in the atmosphere to form carbon 14. The carbon 14 produced is what is known as bomb carbon or artificial radiocarbon. Nuclear weapons testing in the 1950s and 1960s have nearly doubled the atmospheric carbon 14 content as measured in around 1965.
The level of bomb carbon was about 100% above normal levels between 1963 and 1965. The level of bomb carbon in the northern hemisphere reached a peak in 1963, and in the southern hemisphere around 1965.
See this graph, and description below.http://en.wikipedia.org/wiki/File:Radiocarbon_bomb_spike.svg
One of the main methods used to date fossils is by the strata they are found in. Some strata are dated absolutely via radiometric dating. These methods are sufficient to determine a great deal of stratigraphy.
Some fossils are seen to occur only in certain strata (like dinosaurs.) Such fossils can be used as index fossils. When these fossils exist, they can be used to determine the age of the strata, because the fossils show that the strata correspond to strata that have already been dated by other means.
For more information on radiometric dating, read Radiometric Dating and the Geological Time Scale, Circular Reasoning or Reliable Tools? By Andrew MacRae.
Given that the half-life of carbon-14 is 5730 years, one can calculate
that 4 billion C-14 atoms will produce 1 decay per minute on the
average. Converting the 4 billion atoms to grams (a nickel weighs 5
grams), we get 0.000000000000093 grams of carbon-14. Consequently, by
tallying one click per minute on the Geiger counter, we can measure a
whole lot further than 7 decimal places!
A 1-gram, fresh sample of carbon, containing the atmospheric
concentration of one ten-billionth percent of carbon-14, will yield
about 12 decays per minute. That figure follows directly from the
mathematics and, as the atmospheric portion of carbon-14 given above
is an approximation, is close enough to Dr. Hovind's present-day
figure of 16 counts per minute per gram. Because of atomic bomb tests,
the rate is slightly higher today, but the present rate would not
apply to animals and plants which died before such tests. One book
used a figure of about 13.5 decays per minute per gram for the
pre-bomb rate. Consequently, a 64-gram sample of fresh carbon will
still give about 7 clicks per minute after 40,000 years. Because of
background radiation, that's about as far as one can normally go with
this counting method. As noted above, Dr. Dalrymple would extend that
to 50,000 years in special laboratories.
Once again, Dr. Hovind has relied on bad data. If you get your
information from a creationist source, you'd better triple-check it!
Errors get handed down in the creationist literature like the family
jewels!
Dr. Hovind (R6): The shape of the curve of the line is based on too
few real measurements to be reliable. R6. It's not clear to me what
Dr. Hovind is talking about. If he is referring to the carbon-14 decay
curve then he has demonstrated, once again, his ignorance of
radiometric dating.
The decay curve is mathematically determined by the fact that every
atom of carbon-14 in a sample has the same chance of decaying during
each second of time. That much is predicted by quantum mechanics,
which is possibly the greatest of our modern, scientific revolutions.
The random character of radioactive decay is a special case of the
indeterminacy of quantum theory, as was pointed out in 1928 by George
Gamow, Ronald Gurney and Edward Condon. They showed that a particle
held inside the nucleus by a "potential barrier" may be able to
"tunnel through" the barrier and emerge on the other side, since if
the barrier is finite the wave function of the particle is not
completely localized and there is a finite probability that the
particle will be outside the nucleus.
(Brush, 1982, p.42)
Since we are dealing with millions of C-14 atoms in even the smallest
samples, the amount of C-14 remaining with respect to time will be an
excellent approximation of an exponential decay curve. Statistics
assure us of that. Indeed, it would be absurd to speak of the
half-life of a radioactive isotope if it did not have a good
exponential decay curve!
Once we have a good approximation of the half-life for carbon-14, its
decay curve can be constructed with complete confidence. We don't need
Egyptian mummies or what have you at that point. At that point it's
just a routine exercise in math. If you want additional assurance that
we have the correct half-life, then look at the close correlation
between C-14 dates and tree-ring dates (after correcting for variances
in C-14 production caused by changes in the earth's magnetic field).
The snug fit indicates that the half-life of C-14 is stable and
accurately known. Therefore, so is its decay curve.
Today, the half-lives of those radioactive elements used in dating are
known to a few percent by careful laboratory study. So, there's no
problem in getting an accurate decay curve.
-http://www.talkorigins.org/faqs/hovind/howgood-c14.html
All said and done, radiometric dating methods provide a reliable means of determining the ages of critical points in geologic and planetary history, including the age of the Earth, the Moon, and meteorites. That the age of the Earth is billions of years is virtually beyond question because it is supported by a wide variety of independently determined scientific evidence which indicates that the Earth is 4.5 to 4.6 billion years old. Scientists are continually refining this age, but it is highly unlikely that it will change in the future by more than a few percent. In the past, the age of the Earth was the subject of much dispute, but the past few decades have seen the development of new techniques not previously available. There is virtually no dispute among knowledgeable scientists about the antiquity of the Earth and her sister planets.
Creationism
Creationists calculate the age of the earth to be (depending on the sect of creationists,) from 6,000 to 200,000 years old, with the majority coming in at 10,000 years old. These calculations are derived from numerous methods like Thomas Barnes' decay of the Earth’s magnetic field, in his book, "Origin and destiny of the earth's magnetic field." This is a list of the tabulated ages of the Earth. Keep in mind that none of these methods and results are scientifically valid.
When it comes to young earth creationists, in my opinion the most misinformed segment of creationists, the method originally used to calculate the age of the earth (and therefore a max age of the life on the earth,) was using the genealogies from the Bible.
The Bible begins with the Book of Genesis, in which God creates the
world, including the first human, a man named Adam, in six days.
Genesis goes on to list many of Adam's descendants, in many cases
giving the ages at which they had children and died. If these events
and ages are interpreted literally throughout and the genealogies are
considered closed, it is possible to build up a chronology in which
many of the events of the Old Testament are dated to an estimated
number of years after creation. Some scholars have gone further, and
have attempted to tie in this Biblical chronology with that of
recorded history, thus establishing a date for creation in a modern
calendar. Since there are periods in the Biblical story where dates
are not given, the chronology has been subject to interpretation in
many different ways, resulting in a variety of estimates of the date
of creation.
Numerous efforts have been made to determine the Biblical date of
creation, yielding varying results. Besides differences in
interpretation, which version of the Bible is being referenced also
impacts on the result. Two dominant dates for creation using such
models exist, about 5500 BC and about 4000 BC. These were calculated
from the genealogies in two versions of the Bible, with most of the
difference arising from two versions of Genesis. The older dates are
based on the Greek Septuagint. The later dates are based on the Hebrew
Masoretic text.[58] The patriarchs from Adam to Terah, the father of
Abraham, were often 100 years older when they begat their named son in
the Septuagint than they were in the Hebrew or the Vulgate (Genesis 5,
11). The net difference between the two genealogies of Genesis was
1466 years (ignoring the "second year after the flood" ambiguity),
which is virtually all of the 1500-year difference between 5500 BC and
4000 BC. For example, the period of creation to the Flood is derived
using the genealogical table of the ten patriarchs listed in Genesis
5, and 7:6, called the generations of Adam. According to the Masoretic
Text, this period consists of 1,656 years, and this dating is also
followed by Western Christian Bibles derived from the Latin Vulgate.
However, according to the Samaritan texts the period is 1,307 years,
and according to the Septuagint (Codex Alexandrinus, Elizabeth Bible)
it is 2,262 years. J. Ussher agrees with the dating until the birth of
Abraham, which he argues took place when Terah was 130, and not 70 as
is the direct reading of Genesis 11:26, thus adding 60 years to his
chronology for events postdating Abraham.
http://en.wikipedia.org/wiki/Dating_creation#Biblical_creation_dates
Many ancient cultures tried to calculate the age of the earth, and since they didn't have to tools and knowledge that we have now, they usually based it on human record and creation myths. According to one interpretation of Puranic Hinduism, the world is believed to have been created 158.7 trillion years ago.
Conclusion
The dates that science comes up with, when compared to results calculated by Creationists, are far less varied. The scientific date will continue to be defined as new technology and theories come forth, but the main thing is that this result will become more precise.
In science, we collect facts, or observations, we use laws to describe them, and a theory to explain them. Scientific theories are explanations of natural phenomena built up logically from testable observations and hypotheses, and the wonderful part of the scientific method is that it requires repeatability, and peer review.
We rely on the accuracy of science in most every part of our lives, why is it that when science is inconstant with the Bible, some people (a majority of Americans,) reject the scientific answer and use the Bible's?
Another source I recommend reading is, "How Old is the Earth," by Brent Dalrymple