These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Big Lipped Alligator Moment: At one point, Phil goes up at a late showing of Heidi II dressed as the titular character from Bronco Billy along with a woman dressed as Ms. Lily. Who she is, how she knows Phil, and why they're showing up for a movie wearing costumes from a different movie are never explained, but it fits within the mood of just trying whatever in the face of eternal boredom.
Crosses the Line Twice: Phil committing suicide... jarring. Repeatedly committing suicide? Depressing. Him casually recounting this and then declaring himself a god to Rita the next day? Strangely hilarious.
Double Standard: It's arguably present in the unspoken backstory of the film, which explains that Phil was cursed by a woman he'd dated and parted with on bad terms, so she deliberately trapped him in a day he'd complained bitterly about before. Apparently being a jerk in a relationship is a bigger crime than trying to condemn someone to their own personal Hell. (According to the commentary, this backstory was not considered canon to the finished film.)
On a more mundane level, a lengthy montage of Rita slapping Phil across the face is played for laughs.
Ear Worm: Then put your little hand in mine... (Even if you don't find the song catchy to begin with, it will get you through sheer repetition.)
Strike up the music, the band has begun / The Pennsylvania Polka!
Epileptic Trees: One of the more outlandish theories is that Phil was trapped in Groundhog Day for several thousand years. (Although in an earlier, discarded draft of the script, he was.) Harold Ramis estimates that it was closer to about 30-40 years.
It's mentioned someplace (perhaps in the older draft of the script?) that he read the entire Punxsutawney library, every book in it, by reading them one page a day. Each book would take months, if not years, to read; and there would be thousands of them in the library.
This isn't that far out, actually - considering that he learns, from scratch, how to make ice sculptures with a chainsaw, speak fluent French (if not more tongues) and play the piano.
Everyone Is Jesus in Purgatory: Harold Ramis has pointed out that people tell him this film is an obvious allegory for (insert religion of choice here) where Phil breaks the loop after following said religion's key principles.
Though the nature of the reincarnation loop itself and the fact that his goal is to escape it fits Buddhism better than any other religion.
Numerous professional works have also analyzed from a perspective of nihilism and/or existentialism.
"Funny Aneurysm" Moment / Harsher in Hindsight: For a story about self-discovery that involves healing old wounds between colleagues and friends, it's pretty tragic that the friendship between Bill Murray and Harold Ramis got shattered during filming. The fact that they reconciled shortly before Ramis' passing makes it slightly better.
Values Dissonance: As a part of his perfect run towards the end of the film, Phil walks into a restaurant, performs the Heimlich Maneuver on the mayor, saving his life, then turns around and lights a woman's cigarette for her. Public opinion of smoking has come a long way in 20 years.
Vindicated by History: It did okay at the box office and the critics of the time liked it well enough. Within 10 years it would come to be widely regarded as one of the greatest films ever made.
What Do You Mean, It's Not Symbolic?: After the film's debut, the director was called several times by various religious groups, all claiming he was secretly one of them.note In reality, Harold Ramis was raised Jewish, but did not adhere to any organized faith.