Are coffee beans often contaminated with significant amount of DDT? And are those levels known to have any negative health effects?
Depending on where the coffee is grown, it is quite possible it could be contaminated with DDT. In a study by the Smithsonian (R. Rice, J. Ward, 1996), they examined the amounts of DDT and DDD (DDT's toxic metabolite) present in green coffee beans. The limit of detection was 0.001 ppm, and they reported amounts ranging from 0.001 to 0.019 ppm.
There is no 'allowed use' for DDT in the US/Canada as it is banned there (and in 33 other countries) and DDT is only used for malaria control as per the Stockholm Convention. It is a persistent organic pollutant (POP), and is known to both bioaccumulate and biomagnify.
DDT has been linked to poor semen quality in men, and a 5-fold increase in risk of breast cancer in women born after 1931, who were exposed to the highest amounts of DDT before its use was halted in 1972. Prenatal exposure has been linked to a decrease in cognitive skills in preschoolers when the cord serum contained DDT in excess of 2 ppb (ng/ml). Researchers are also studying the possibility of a link between pesticides and autism
Given the half-life of DDT when mixed into the soil (between 5-8 years, taking between 25-40 years for a 90% reduction in DDT levels), it is possible to still find residue on produce today. The International Agency for Research on Cancer (IARC)'s report on DDT can be found here. They've classified it as a 2B - Possibly carcinogenic to humans. They also list the maximum allowed DDT residue limits for a number of countries.
Now - what constitutes a 'significant' amount? It depends on the context.
The drinking water guidelines (according to the IARC report, above) list the WHO limits for DDT of 1 ug/L (1 ppb), and the US EPA allows 2.85 ug/L (2.85 ppb). The report doesn't list coffee limits for the US, but other beans for other countries are listed between 0.05 - 7 mg/kg (1 mg/kg = 1 ppm in soil).
For drinking water standards, the amount of DDT on coffee beans would be significant. For foodstuff standards, it is not considered significant.
As far as negative health effects - there is no definitive cancer link for human exposure to DDT (plenty of animal studies, however). Toxnet lists a number of studies delineating the body burden of DDT - all of which are much greater in concentration than what is found in those coffee beans.
For healthy adults, the risk posed by those concentrations would currently be considered small, as exposure to DDT is not solely restricted to coffee beans.
There's still so much we don't know about the long term effects of DDT, to be honest - but then that's the case with many chemicals we use today.