Why doesn't Lupin become a werewolf the night Harry looks for Peter on the map? The moon is out that night.
There is no indication that there is a full moon on the night that Harry encounters Snape and Lupin, and the very fact that Lupin is human would indicate that it is not. There is definitely moonlight coming in the windows in Harry's bedchamber and Snape makes a snide comment to Lupin about "taking a walk in the moonlight", but the moon could still be bright and visible without being full.
Good question. From my perspective, in the book, Snape mentions that he was bringing Lupin the Wolfsbane potion but ended up following Lupin because he saw him leave the castle. In the movie Sirius asks him if he had taken his potion when they realize its a full moon. So to answer your question it could have been the wolfsbane or it could have been the full moon.