Creator Breakdown: Bill Murray was going through a divorce during filming, which, coupled with arguments with Harold Ramis over what direction the movie should take, led to their friendship breaking down.
Enforced Method Acting: See Mistaken for Gay below, and then realize that that scene was improvised by Bill Murray; Ned's reaction was largely genuine. Stephen Tobolowsky (who plays Ned) is a great character actor, and did plenty of improvisation in the film, too.
As is usual for Bill Murray, when Rita slaps him, she really does hit him hard. Not surprising, since all of the abuse Murray suffered from Carol Kane in Scrooged were real as well.
Shrug of God: How long Phil spent in the loop. Harold Ramis said it was 10,000 years, while Bill Murray mentioned they discussed it and decided on "about ten years" (widely thought to be the "correct" answer).
Throw It In: After Phil smashes the radio, it keeps playing "I Got You, Babe". However, that wasn't supposed to happen. It was such a wonderful, dark moment that Ramis left it in.
Type Casting: Mostly Bill Murray, alternately played straight and inverted during the course of the movie, but a couple of the others could be described as such too.
Roger Ebert: The Murray persona has become familiar without becoming tiring: The world is too much with him, he is a little smarter than everyone else, he has a detached melancholy, he is deeply suspicious of joy, he sees sincerity as a weapon that can be used against him, and yet he conceals emotional needs.
What Could Have Been: The original script featured the explanation for the unending loop and its escape clause, but they found by leaving it out made the film more magical.
Considering the original explanation involved a curse by an ex reading a "how to do magic" book, it's less "making the film more magical" and more "removing the idiocy".
They flirted with the idea of a Darker and Edgier film, by taking full advantage of the no consequences mentality, (major cruelty, murder etc.), but they decided not to, realizing a more light-hearted comedy would appeal more to the general audience.