An easy thing to notice is if an actor says a complete line of dialog while the camera is on someone else. Usually this will happen at the very begining or end of a scene. Sometimes it's exposition, like if a scene was cut and they need to explain how the characters got from point A to point B. This is just a hunch, but in a recent episode of Bones Booth and Brennan have an indepth conversation while riding a motorcycle. I think some if not all of that dialog was looped in because a scene was cut. I can't remember exactly what was said, but I remember thinking "I wonder if they cut a scene" while watching it. The camera was too far away to really be able to see their mouths.
In shows like Bones or House, when there is a lot of technical information being thrown around, a line is sometimes looped in to simplify what's going on. Tonight I was watching an old episode of House and I noticed an ADR. Foreman comes up to house to tell him a blood sample from a 6 year old contained endomitrial cells. Anyone with an understanding of a woman's body would obviously know what that means, and it's made perfectly clear in the very next scene. I guess they really wanted to keep the audience up to speed, because they cut to a shot of House while the line "It's menstrual blood" is looped very well by Foreman. Er, I mean Omar Epps. I've seen that episode tons of times and this was the first time I noticed the looped line. One excellent example that I may never have realized was a looping (I learned it was from the commentary) is in the Firefly episode Out of Gas. In this episode the ship has broken down and the crew is running out of oxygen. Mal asks Kaylee how long they have. "A couple hours, maybe." The camera cuts to Mal for the ADRed line: "We'll start to feel it... and then we won't feel nothin at all." The look on Mal's face fits perfectly with the line, and I would never have realized that the line was added in after the fact.
It's a fun game, but let me warn you: If you're the type of person who doesn't like to think of the process of making a TV show, don't play this game. I'm the type of person who finds things more impressive once I know how it was done. It's why magicians piss me off. Knowing how a trick is done actually makes it more interesting to me, and if I can't figure it out I find it frustrating. So, for me, little glimpses into the making of the show and trying to guess why the director or producers felt the lines needed to be added is super interesting and makes the show better. If you're the type of person that just wants to watch, and not know the magician's secrets, don't try to spot the ADR.