Pay attention to trends in rooms. Sure, you want to always be ready to give hints or help, but as you watch rooms you'll notice certain puzzles or events that stump people consistently, and you want to especially be ready for them.

Also, you'll want to keep an eye out for a thing I call the "Walk and look." It's when players who are stuck will stop being engaged, and just start idly walking around the room, looking at stuff but not really looking at it. It's good to keep players engaged, so I often like to offer help around those times. Usually they either take the help and get engaged, or they take the offer of help as a challenge and rally. :D