Accidentally Accurate: They once did a parody of Cathy called Amy!, which depicted Amy Winehouse hiding drugs in her beehive hairdo. Then someone filmed her pulling a vial of cocaine from their hair, and suddenly, it's like they knew.
Actor Allusion: In the movie / TV parodies, there are many jokes related to this.
Hey, It's That Guy!: Very many freelance artists and writers have worked for the magazine, so their art is often recognizable outside it.
Mort Drucker, Jack Davis, Bob Clarke, and Bob Jones (among others) are all freelance artists who have done countless ads. In fact, when they did a parody of the Esso "tiger in your tank" ads, they almost had Bob Jones draw it until they realized that Jones drew the real ad.
Paul Coker was a character designer for Rankin-Bass. His loose, scratchy style is quite recognizable.
Writer Dick DeBartolo is the host of the Daily Giz Wiz podcast, and was a longtime question-writer for Match Game.
Several artists and writers and artists jumped ship from Mad to its rival Cracked. Most notably, artist John Severin left Mad shortly before the end of the comics era, and quickly became the flagship artist of Cracked. Longtime writer Lou Silverstone also left for Cracked in 1990, as did Don Martin (of all people!).
Old Shame: Mad lent its name to an Animal House-style comedy, Up the Academy. After it did poorly at the box office, Mad was quick to disown it, and wrote a two-page satire of their own movie, which ended with the entire staff fictitiously quitting in shame. William M. Gaines also paid Warner Bros. $30,000 to remove every reference to Mad from the movie. However, following the sale of Mad to Time/Warner, the references were restored on all recent TV airings and the DVD. But it's still Old Shame to the Mad staff.
Some characters in parodies refer to their previous roles as such. In the parody of "Eraser", Arnold's character is asked to "erase" some of his co-stars' previous roles, and he tells them to wait until he's done with his own.
The Other Darrin: After Antonio Prohías left the mag, Spy vs. Spy went to other artists. Bob Clarke drew the work from 1987 to 1993, usually with Duck Edwing writing the gags. After Clarke quit, George Woodbridge did two installments in 1993 with uncredited writers, then Dave Manak took over art duties until 1997, again with Edwing usually serving as writer. Other writers who pitched in during Clarke's and Manak's tenure included then-editor Andrew J. Schwartzberg, and Michael Gallagher, who worked with Manak on the first issues of Archie Comics' Sonic the Hedgehog. (Manak and Edwing also handled a very short-lived Sunday Strip adaptation in 2002.) Peter Kuper has drawn the feature since 1997, and does the majority of its writing.
This has also shown up in Monroe and..., which was originally drawn by Bill Wray (the same one who worked on Ren and Stimpy in the 1990s). After a short retirement, the feature was briefly revived with Tom Fowler as the artist before retiring again. The change in artists was supposedly because Wray (who, like most of the staff, has plenty of work outside the magazine) had very little time to draw and color the strip on time, meaning that he had to do a rush job.
The cover to issue #212 (Alfred skiing and crashing into a tree) was conceived by Norman Mingo, who started it but never got around to painting it before he died. Jack Davis ended up drawing it instead.
"Celeberity Cause-of-Death Betting Odds'' was originally drawn by Thomas Fluharty for its first few issues. After he left, James Warhola drew one, and Hermann Mejia took over (barring one-time returns each by Warhola and Fluharty, plus a four-issue stretch where Jon Weiman drew them instead) until the series was relegated to the "Fundalini" pages.
Also present in the Star Wars parodies. Dick DeBartolo and Nick Meglin co-wrote the A New Hope parody, with Harry North as the artist; the next four had just DeBartolo writing and Mort Drucker drawing. Inexplicably, the last one switched to David Shayne for the writing and Hermann Mejia for the art.
Too Soon: Issue #411 (November 2001) was originally supposed to have a cover featuring Alfred mistaking crime scene tape◊ for the finish line of a race. The cover was deemed insensitive after 9/11, so it was hastily pulled and replaced with a stock Alfred image photoshopped to have an American flag in place of his missing tooth. A few copies of the original cover supposedly got out, though.
According to this interview with Fold-In artist Al Jaffee, he created a Fold-In themed to the 2012 theater shooting in Aurora, Colorado, and the editors decided that it was in poor taste, and 600,000 copies were shredded to cover it up.
Writer Revolt: A running joke in the magazine, and somewhat true behind-the-scenes occasionally.
Write What You Know: Dick DeBartolo was working for Mark Goodson Productions when he was tapped to write the Family Feud parody. Naturally, he took that opportunity to knock down every trope that show presented (and submitted the parody under a pen name).