If I can offer you one piece of advice about how to watch TV, it's this:
I have had a number of different roommates in the past, so I know that people who aren't accustomed usually find it annoying at first. But let me tell you, it's worth it.
One of the reasons is alluded to in this node, but it just scratches the surface. I have been regularly watching TV with captions on since 1994, and here are some of the things that I've noticed.
Not in an interference-induced typo kind of way either. Many times I have been watching a sitcom and when the punchline arrived, the spoken line was completely different from the captioned one. Usually, the captioned one tends to be racier or more outrageous. My hypothesis is that last minute rewrites are not uncommon, but that offline captions are developed from original scripts. This happens particularly often with The Simpsons. An example1:
When Homer fails to blow himself up at a town meeting...
Homer: Nice wiring, Bart.
Bart: It worked on the test corpse.
Bart: It worked on the test goat.
Dialogue and sound effects are sometimes inaudible
This occurs less in sitcoms and more in drama and mystery shows. Sometimes dialogue is mumbled, sometimes it's not spoken at all. I personally think it's interesting to experience the story as the screenwriter indented.
Mainly the spellings of obscure words, but sometimes other stuff too. Before I watched closed captioning, I didn't know that thing was called a raspberry. You're still going to have to study for your GRE, but I like trivia almost as much as minutiae.
You miss less
Living with roommates, I have often tried to watch TV while others in the room were being really loud. However, I'm not antisocial, and with closed captioning on, I won't miss a line of Law & Order.
This mainly occurs when the reception is poor, or when captions are being done in realtime (e.g. a live sporting event). When captions get messed up, the results are often highly amusing. As I understand it, one of the reasons is that realtime captions are entered using a machine similar to court stenographer's. The entry system is phonetic rather than alphabetic, and a computer is responsible for converting the output to normal text. A small error usually results in the computer selecting words which are phonetically similar, but utterly nonsensical2. This often happens with proper names as well.
1I'll add more when I remember them, or when people tell me
2I'll put up some examples the next time I notice them