Hi Marco, actually, this is a very valid question. As others have mentioned, when I stop by a table, I first try to check whether life totals match and there is nothing illegal (illegal enchanting…) or unclear (various tokens - ask the player what these are supposed to represent and find those in your pocket). A good idea is also to ask what is the current match score (i.e. which player would be more likely to try some Stalling tricks).
Once familiar with the match in progress, I try to follow the game by rules perspective. Ideally, any game play error should be caught before it can cause any major problem that cannot be easily fixed. Check that correct mana is spent, a player delved enough cards, illegal blocks are not accepted, a player does not draw extra cards…
If it is a Standard tournament soon after the Standard rotation, it may also be a good thing to check players' hands for any illegal cards (it may look funny, but it has actually happened :-)).
A very important thing is to somehow keep track whether players played their land for the turn. Just because it is so common question from them. I usually use my pinkies to do that.
I think there used to be a great article on the topic on Kevin Desprez' blog. I suggest to read that.
Edited Milan Majerčík (Oct. 10, 2016 04:11:31 PM)