Our last game vs. Oak had some questionable usage of time outs in the 1st half. Not sure what was going on, you might want to look at that.

Is there a small random chance of burning a TO on wrong personal / lining up wrong?

Yes, there is - if a timeout is taken when you are not in a hurry-up situation that is what happened.

In the game today, I was a bit puzzled as to why, on the while final drive of the game, with my team down by 3 and running the 2 min drill, my team used no timeouts until 2 seconds left? We drove the ball perfectly and could have gone for the winning score if they used timeouts, and not kick a FG on a 1st down.
http://mfn1.myfootballnow.com/watch/2797#498530

The logic I had implemented has you running the clock down once you're in field goal range at the end of the half, or at the end of the game if you are down by 3 or less. I'll make an adjustment to the logic so that the end of the half doesn't consider that at all, and you'll only drain the clock if you are down by 2 or less, so you'll continue to try for a touchdown if you're down by 3. This may result in you leaving enough time on the clock for the other team to score after you end up kicking a field goal, but should solve some of the issues that have risen from the current logic.

(This code is still only in MFN-1 btw, the other leagues don't have any of this "run down the clock to prevent the other team from coming back" logic)

On a related note...

If you're down at the end of the game and stop the opponent on third down, shouldn't the defense call a TO to preserve clock?

I have posted a couple of situations where this logic wasnt working in other leagues. Both times I was trailing at the half, once by 7 and the other but 3 and i let the clock run down with using only 1 time out just to kick a FG. You commented on one about a 4th down but I never had a 4th down on any of the examples
http://mfn1.myfootballnow.com/community/1/233?page=1#1802