How much does it hurt one's application to try the GRE again?
The first score will very likely not matter if you do better the second time.  Most programs look only at the best score a student has on their record.  Officially, that's what my program does.  Unofficially, if you had a really low score the first time you too the exam, it would raise a red flag, and we might go looking for some other reason not to admit you.  However, an 82 percentile on the first try, if you take the test again and do better, is not going alarm anyone.