The Vikings burying the chest containing the mask on an American beach.
Peggy's death after betraying Stanley, where Dorian (who has the Mask on) hurls Peggy into a printing press, gets mashed inside of it, and comes out as a bloodied newspaper reporting her death. Because of that, Peggy just disappeared from the plot after getting her money and didn't get what she deserved, though, had they kept that scene in, it probably would have given the movie an "R" rating, and there would be a Continuity Snarl in the animated series, where Peggy is alive and well, and still remembers the time she betrayed Stanley.
An extended scene concerning The Mask's confrontation with a street gang.
An early workprint of the movie can be found online which has more extended/deleted scenes not available on the DVD. One of which is a scene that shows Stanley getting dropped off by his apartment after finding The Mask in the Edge City river, and is immediately confronted by the same street gang that he would see again shortly as The Mask. The gang's leader asks Stanley for the time so he can steal his watch, foreshadowing how Stanley would soon get payback on him as The Mask when asked the same question.
With that in mind, remember this exchange?
Mrs. Peenman: Ipkiss! Do you have any idea what time it is?!
Ipkiss: Actually, no.
Doing It for the Art: Carrey went to the extra trouble of practicing how to talk/act while wearing the Mask's enormous fake teeth, to enhance the comedic effect.
Executive Meddling: Very surprisingly inverted, at least if one listens to the DVD commentaries/behind the scenes material. Chuck Russell — director of A Nightmare on Elm Street 3: Dream Warriors stated that New Line was interested in developing "The Mask" along the lines of the comic books; this would have become, according to Russell, "the next Freddy Krueger". But, he noted, that draft after draft of the more comics-faithful adaptation simply did not work. So, he fought valiantly to make "The Mask" as a comedy; the Cuban Pete sequence is one of the few elements that survived until the final cut.
There were plans for an actual sequel (not, Son of the Mask, mind you). One idea was that Lt. Kellaway finds the mask, dons it, and becomes the next villain. Furthermore, Nintendo Power actually had a contest that whoever won could appear in the film as an extra. They Lampshaded this in their final issue.
Expy: Doyle (Lt. Kellaway's partner) looks like a cleaned-up, less pathetic (but still kind of dim) version of Bill Dauterive from King of the Hill.
Hey, It's That Voice!: A lot of the familiar 1990s kids' cartoon voice actors appear here, like Tress MacNeille (Mrs. Peenman), Rob Paulsen (Stanley Ipkiss/The Mask), Frank Welker (Milo the dog and the next door neighbor's baby from "Baby's Wild Ride" and "Mutiny of the Bounty Hunters"), Jim Cummings (Kellaway's partner Doyle, Kablamus, and a lot of one-shot characters), Kevin Michael Richardson (Mayor Tilton), Cree Summer (as Cookie BaBoom and various background characters), Kath Soucie (as various background and one-shot characters), Cam Clarke (as Eddie/Fish Guy and Smedley the Mayor's assistant), Neil Ross (Norman Osborne/The Green Goblin of 90s Spider-Man fame, countless heroes and villains of GI Joe, Transformers and other 80s favorites) as Kellaway, and Tim Curry (Pretorious).
"Split Personality" had Dan Castellaneta (the voice of Homer, Krusty the Clown, Barney, Arnie Pie the hapless helicopter reporter, the Squeaky-Voiced Teen, Grampa Simpson, Groundskeeper Willie, Sideshow Mel, the Spanish Bumblebee Man, and Homer's male relatives on the season nine episode "Lisa the Simpson") as the voice of Chet Bozzack, the bully who harassed Stanley in high school. You can tell it's him because the evil side of Chet sounds like Krusty the Clown with a more gravelly voice.
Keep Circulating the Tapes: There are only three VHS releases (back when VHS video and VCRs were popular) and the two-part episode "The Mask is Always Greener on the Other Side" was released on DVD along with The Mask around the time that Son of the Mask was released in theaters. Other than that, the entire series hasn't been released officially on DVD (though it was announced that the show would see a DVD release in 2013 thanks to Shout! Factory). All is not lost though — most of the episodes are available via torrent downloading and on video websites like YouTube and Dailymotion and the show did rerun on Cartoon Network and Boomerang channels in the UK and Australia.