Being a USAF Combat Arms instructor these days, I have watched idiots that weren't paying attention in class pooch-screw an M-16 every way possible putting them back together and leaving out the firing pin or installing it with the flange on the wrong side of the firing pin retaining pin isn't as uncommon as you may think. The tapping with a mallet method you found is one way to fix it. Pulling back lightly on the charging handle and pressing the carrier back into battery until the cam pin aligns itself correctly is another but really, it's just a matter of bump, wiggle, jiggle and tap until it comes out. Just be patient.
Another thing I have seen is forgetting to put the buffer and spring back in. Go to do a function check by pulling the bolt back and it stays there. Kind of funny to see the look on their faces!
The easy fix for this in the event you do this let gravity work for you by tapping the muzzle on the ground and the bolt carrier moves back forward so you can break it down and put the missing spring and buffer back in.
Another trick I teach is when putting the bolt back in, the cam pin will go in only one way since the wrong end of the cam pin hole in the bolt is designed to prevent you from putting it in wrong. A simple trick that works every time is how we learned how to do this in the dark when I was in the Marines and that is to hold the carrier in your right hand with your index finger along the side of the gas key. Now when you put the bolt in, feel the locking lugs and as you rotate it, your finger will eventually drop down onto the extractor. Now your cam pin will go in every time because that is the correct orientation the bolt needs to be in to get the cam pin back in.
As far as forgetting to put the cam pin back in, yes you can assemble the rifle without it and you may even be able to load and fire 1 round. I say that because without the cam pin, if it is in a position to fire with a round in the chamber, the lugs aren't locked and now you have a blowback operation in a locking lug design!
The comments about the weapon blowing up are technically correct since while the explosive power of the cartridge should mainy stay in the chamber, the bolt now comes back with all that 52,000 PSI and no way to control it resulting in a destroyed weapon and possibly a destroyed shooter as well. If however, the term "explode" doesn't tickle your fancy though, think of it as an "unplanned catastrophic weapons disassembly not in accordance with approved methods."
