I have two pet rabbits that I keep in a large size, solid bottom dog crate. (I can almost fit inside of it myself) The spaces between the bars are just right, and at a young age they cannot get out. BUT, there is one gap closest to the door that is bigger than the rest, and my most curious baby found it.

This morning I found him outside the cage completely. His head fits through the hole, but his legs get stuck and he has to pop them out. It looks dangerous on his part, so I covered the holes.

Now, I am noticing he has a limp on one of his legs and doesn't put any weight on it. He still scoots around, (no hopping/jumping) and eats/drinks/uses the bathroom frequently. I picked him up and examined his legs by stretching them out and pushing them back in. He doesn't seem to mind, so I am confused.

What should I do?

Bunnies will hide their pain and discomfort because in the wild it means sure death. Domesticated bunnies have the same instinct. If you noticed him limping a bit and you know he can wiggle through the space, I would take him to the vet and have him examined.
I have seen bunnies "totally healthy" die because of tumors and internal injuries bc their owners didn't take notice of the very subtle body language.
When he's laying down does he favour one leg over the other? Do you see him grinding his teeth?