Bill Murray was bitten by the groundhog twice during shooting. Murray had to have anti rabies injections, because the bites were so severe.
According to Director Harold Ramis, most of the time, when he tried to explain a scene to Bill Murray, Murray would interrupt and ask, "Just tell me - good Phil or bad Phil?"
Harold Ramis originally wanted Tom Hanks for the lead role, but decided against it, saying that Hanks was "too nice."
(at around 59 mins) The scene where Phil picks up the alarm clock and slams it onto the floor didn't go as planned. Bill Murray slammed down the clock, but it barely broke, so the crew bashed it with a hammer to give it the really smashed look.
All the clocks in the diner are stopped, mirroring Phil Connors's predicament.