In the movies, fingerprints identification always works, with no mistakes. How close is this to reality?
Properly done, the false positive rate is negligible (estimated under 1:60 billion) assuming that the axiom "fingerprints are individual" is correct in the first place.
Using automated matching, the error rates are MUCH higher, especially on partial prints, which the police uses too. Because the false positive rate on those are known to be horrendous, all automated matches are verified manually (though that does not really make it any better). All in all, false positive rates of between 1% and 4% are not uncommon, depending on the investigator's diligence.
You should note that identifying a person without doubt is not the intent of matching a fingerprint in the first place, nor is ruling out a possible suspect.
Like most forensic "evidence" (such as a DNA sample), fingerprints don't really mean an awful lot, though they are often seen as "unquestionable".
For example, your fingerprint on the knife that sticks out of a dead body can equally well mean that you've killed that person or that you've had that knife in your hands in the shop two days ago (you thought about buying one). Your DNA on a cigarette that was found at a crime scene can equally well mean you're the culprit and stupid enough to smoke mid-crime, but it could equally well mean you threw the cigarette on the street the day before, or someone took it out of the ash-tray in your favourite cafe, just to lay a false track against a random person.
While it is true that often things indeed are what they look like, they need not be, and sometimes they aren't. However, it is usually assumed that the "evidence" is infalliable, which is an increasing problem in a society where the classic presumption of innocence has turned into "you must prove your innocence".
EDIT (some sources were asked for):
One source which is freely available online is Galton's somewhat dated book. Don't be put off by the fact that the book is 130 years old. Galton gives somewhat divergent numbers for different numbers of matches in particulars, they're somewhere in between 2^29 and 2^41, but all of them are in the same "close to zero" range. That's for a careful examination, assuming the examiner is not "faulty" in himself (which certainly does not apply to automated systems).
I cannot find a reference for the 4% now... you'll have to take my word for that it was in some paper a couple of years ago... :(
The Marion Russ murder is a famous example of how wrong things can go with unfalliable evidence. The arrest of Brandon Mayfield in 2004 for the Madrid bombings is another.
False rejection and false acceptance rates on automatic matching can be somewhat estimated from data sheets available at biometric lock manufacturers' websites. It has to be said that a forensic computer is somewhat (2-3 orders of magnitude) more accurate under optimal conditions, since it does not have the same time and computational power constraints, but the world is rarely ideal, either. If the input quality varies by 3-4 orders of magnitude, then the output quality obviously does, too. So... again, numbers must be taken with a grain of doubt. But anyway, rough figures.
(As far as I'm concerned personally, I would multiply any claimed numbers by a factor of at least 100. Most manufacturers claim FRRs and FARs of <0.1% and <0.001%, respectively, some claim 1/10 of that. I'm seeing a false rejection about twice per day, at <0.1%, that would be 2000 attempts. Not only would that mean that I'd spend a full hour every day with it, but also my finger would be bleeding... this just isn't realistic.)
Not very since on most crime scenes you will only find partial or bad prints. The number of mistakes is pretty high. Especially when you are on the wrong side.
As with all things forensic it is the interpretation that is all important, these day more and more forensic experts use a Bayesian approach to interpreting the data. Meaning that they do a pre-evaluation before starting the analysis and then at the end seeing which one of the hypotheses corresponds with the pre-evaluation the most.
I'm pretty sure that this is not done with fingerprints because of the common use of this techniques. This because it is cheap and can be automated.
It is also a question of how strict they can be. For example a partial print will be put throught the computer and it might find another fingerprint in tha database that has 5 common points. This would be low for a complete print where they would speak of a match after 12 common points.
So in the forensic world (I work in a forensic textile lab) everything should be about interpretation, interpretation, interpretation. The same results might lead to another conclusion based on the context and the context might change in the course of an investigation because of additional evidence, added witnesses or changing declarations.
But never forget prisons are full of innocent people.
In Germany the Chaos Computer Club developed a cheap technique to copy fingerprint based on a photograph of the correct fingerprint from a glass bottle.
Some people also don't have clear fingerprints and the commenly used technqiues don't work with them with the same certainty that the work with people who have clear fingerprints.