The game is meant to be played a certain way. Mandatory triggers are the responsibility of both players to be handled properly. It is just as much your responsibility to make sure they have the correct mana to cast their spells and it is theirs. It really only benefits you to be spot checking their work. If there is an error, you should call a Judge.

If you notice an error and choose not to point it out (cause its really bad for you if done correctly) it could end up being bad for you. However, if the trigger is optional (up to X creatures or you MAY do something) you are not obligated to point out they missed it. I wouldn't want to point out my opponents optional upkeep trigger the first time they missed it, for fear that they catch up next turn.

The bottom line is that there is a fine line between what you can let slide, and what needs to be addressed and fixed. You do not need to play their deck for them, but you do need to make sure the game is being played by the rules. If you are ever not sure, just call a Judge, that's why we are there.

So, how obligated am I to point out my opponent's mistakes? I mean, do I have to play his deck for him? Do I point out his missed non-may trigger every time, or am I supposed to call a judge over instead?