Barnaby: Troy, you are about as politically correct as a Nuremberg Rally.
Troy and Jones being introduced, after the former nearly runs the latter off the road. In fact, Troy's driving in general is pretty hilarious in and of itself.
"Dead in the Water", during which Scott and Barnaby must often cross rivers, and the only way to do so is via rowboat (and guess who gets to row...) When Scott arrests a guy, he brings him back via rowboat, with an unbelievably smug expression as he finally gets to sit back.
There's a case in a village which has people who like to role-play. At one point Barnaby is walking in the woods and hears a woman calling for help, Barnaby finds her, in a gown fit of a princess, and there's nothing wrong with her. A man turns up with a gun and dead rabbit in hands and seems confused about Barnaby being there and then a second man with a camera arrives and when the first man asks who the second man is and Barnaby tells him that it's her husband. The man with the gun says, "Her Husband", in a disbelieving voice and then turns round and runs off.
From "The Axeman Cometh":
Barnaby How old do you think I am? Jones I've done speed dating, not carbon dating.
Later on, after Jones and Barnaby pass a bongo player in the street.
Jones: Can I arrest the bongo player? Barnaby Only if you promise to break his fingers.