Hunduh --
I applied as a volunteer LEO (Level III Reserve) with my city. I was requuired to undergo all POST requirements, including a thorough backround investigation. The polygraph is required of *all* applicants, even those LEO's who have retired and reapply as "dinosours" (part-time investigators for performing backround checks, etc.).
It's natrual to be nervous, and the polygrapher knows this -- especially if it's your first one. Like you, I tried marijuana in H.S. and had a run-in with the law when I was 16 years old. I don't think they're looking for someone who is "squeeky clean", but someone who is honest. Interestingly, I told the polygrapher that I had only 2 hours sleep the night before (I work in cardiac surgery) and was very tired. He told me that my response to his questions would be measured slower, which is somewhat in my favor if I were lying. Not that it really mattered, but it was a consideration.
Besides the typical drug questions, he asked if I had ever forced sex on another person or had sex with animals (I'm not joking, although I found that question quite funny ). There were also questions about stealing from employers. It's a very sensitive test, but it doesn't tell whether you're telling the truth. It just reports any physiologic response you have to hearing a question. If he asks you about a response you had to a particular question after the test, just say that you felt "burned-out" or you were loosing your concentration. I'm sure it won't be counted against you if it's a minor blip on his graph. I don't think that anyone has ever passed a polygraph because of all the false negatives that are recorded. Just relax and get through it.
Good luck and let us know how it turns out.
-- Ale