Everything that everyone else has said is great...and like they have all said, it's a skill that takes time.
If you didn't get to tech the show yourself and thus didn't get that time to really study all the tech elements, my two cents is this:
Start with those times when you see something off and think it is wrong. Ask your crew in the moment if something is different - like Matthew said, question everything. If they say yes, something is off, then they can give you specifics so you know for next time (like if a specific lighting fixture is out of focus, etc.). BUT, if they say no, nothing is wrong and your gut says otherwise, write it down anyway. This way, next time you call the show, you can take a close look at that section and see if it happens again. If it doesn't, obviously there was definitely a problem one of the times. Clearly, this won't work for things like a burned out lamp because if it's out, then the lamp will just still be out, but with moving lights that occasionally don't hit their focus or something odd in an audio mix, etc., it can be helpful.
You can alternately ask what the thing is supposed to look like, rather than asking if it is wrong (like asking what the focus is supposed to be doing with a lighting cue, or how the prop presets).
You'll also learn about your crew, and their willingness to tell you when something is wrong. I once worked as an ASM with a head electrician, and every time I called the show and asked him if something was off focus, he would say no. Then after the show, my PSM would tell me, in fact, my hunch was correct and something was off focus. So I would just write it down and then I would know for sure the next time.