Maybe he was DQ'd for one of the things you mentioned. Even stealing gum once, let alone up to four times is stealing and his age at the time of incident would make a difference. Stealing at five is different than stealing at 15...Or, like others said, maybe there was something he told them that isn't necesarily written down in the packet nd raised a flag to them.
Or maybe you're interpretting 'not selected' as 'disqualified.' As others also pointed out, there is a difference. DQ happens only for lying about something in your background or having something in your background that is disqualifiable. If he was DQ'd for background, he can try another department that doesn't consider whatever did a DQable offense. If he was DQ'd because he lied, then he's going to have a tough time because LEO's are expected to be honest, and he's already lied once in the process (and anywhere he applies later will find out why he was DQ'd from where he applied before).
Now, if he just wasn't selected, then it could be for any number of reasons. Any of the things you mentioned look bad enough if someone else has never done those things.And then there's sheer amount of experience. While it's admirable that your son was an Explorer and is pursuing a degree in a field he's passionate about, he's only 18 and only been an explorer and started a degree. There are others he's in competition with who are older, have four year degrees, even masters, and/or military experience. If you've only got a few open slots who are you going to take? So, if he was only not selected, I'd say he's on the right path, just keep himself clean (and away from friends who do drugs), his grades up, etc. and apply elsewhere once he's got a bit more experience under his belt.
We must all fear evil men. But there is another kind of evil which we must fear most, and that is the indifference of good men.
-Monsignor, Boondock Saints