You can easily fix that with a dremel tool (or your contractors) - I'm assuming you are referring to the quarter round?

I believe they are referring to the door trim at the floor--the "hairy" appearance of the cut.

yes you are correct, i was referring to the jagged wood.

is that supposed to be caulked and what kind of caulk should i use?

It doesn't need to be caulked. But, if you do, you can pick clear, white or wood tone... I probably wouldn't notice it most of the time.