Saw one eat a rocking chair one time...

Quint caused his first wife's "demeez" by tossing her overboard when she was sitting in the chair. Quint was being half-truthful when he said he saw a shark eat the rockin' chair, but he was lying by omission by leaving out the "demeez" story, whose prime component was Mrs. Quint as a shark snack.

Rocking chairs are surprisingly tasty, even though they count as a vegetable.

I think we may have another shark problem.

Funny line, and also consistent with everything we'd heard before that about how sharks are mindless eating machines. The scene with Brody and Hooper performing the half-assed autopsy on the tiger shark has a whole exchange about it.

Hooper: "Just like I thought...came up the coast from warmer waters." Finishes wiping off license plate and tosses it to Brody.
Brody (incredulous): "He didn't eat a car, did he?"
Hooper: "Sharks'll eat anything...."

And so on. So much memorable dialogue in this movie, a lot of it very funny. It was one of the things that endeared me to the characters.

Not sure if the shark was actually eating the rocking chair. Maybe it just needed a toothpick.

I'm pretty sure that Quint was joking. It was just a fancy way of saying that a shark will eat anything.