Paris has what's called a "hanging" collumela. The collumela is that little bit that that separates the nostrils into two holes. The slimmer the nose is made to be, the more apparent a hanging collumela will become. The surgeon did not touch that part of her nose, she was born that way. Some people elect to get it "trimmed" as part of the whole nose job package, Paris has opted not to.
There's nothing wrong with it, it's genetically determined if you have one, just like it's genetics if you have a free-earlobe or attached earlobe. That's just one of the things that makes us all unique.
Her before vs. after though, it's hard for me to say. Her lips before were good, her "after" nose I am on the fence about, the buccal fat removal really did mature her quite a bit from the previous baby face. I would be inclined to say had she gone for a less severe blepheraplasty, she would be able to age much better without having a "hollow eye" socket, and she may have been able to avoid the eyelid ptosis injury the surgery caused her.
I dunno, to me it's a toss up. However, I do like her brown eyes. It made them look much bigger than the blue beads she's sporting now.