The #1 problem with dry hopping is the introduction of oxygen. When you drop those pellets in they will drag o2 down with them. On commercial batches I have been using a 15 gallon yeast brink, adding all my hops and then purging that vessel with co2, letting some beer flow into the brink from the tanks and then blowing that back into the fermentor with the hops. This vastly improves shelf life and hop flavor stability.
If you have c02 you can add your hops to a secondary vessel (carboy or corny keg), purge that vessel with co2 and then rack your beer onto the hops to the same effect I mentioned above. Or you can add the hops to the primary vessel just near the end of fermentation so that the yeast scrubs the o2. Arguably if there is still yeast in the fermentor you will have a different hop character like Denny mentions. There is actually a theory out there called "Bio transfomation" which is what the "cloudy IPA" rage is all about but you will have to google that for more info.
The other problem with that latter method is you can expect to lose some hop flavor and aroma when the yeast eventually settles out because the hop resins bind to the yeast cell and fall out with them.
I will edit this to add: I tried to get away from dry hopping but there is nothing to compare with that aroma. It is well worth it.