Actor Allusion: George Costanzo (best known as Harvey Bullock from Batman: The Animated Series) has a cameo in "Columbo Goes to the Guillotine", playing a bar owner who happens to be a retired police sergeant. Costanzo was a police officer before he became an actor.
Actor-Shared Background: Columbo tells a police officer helping him in one search that "Three eyes are better than one," implying that Columbo has a false eye just like Peter Falk.
"No Time to Die" is an adaptation on the 87th Precinct novel So Long as You Both Shall Live, with Columbo taking the place of multiple 87th Precinct cops (in the novel Bert Kling's new wife Augusta is kidnapped on the day they're married, in this adaptation it's Columbo's nephew's wife who's taken).
"Undercover" is also an 87th Precinct adaptation, of the novel Jigsaw. Unlike the above, this version includes one of the characters from the 87th (Arthur Brown, who's also one of the cops investigating in the book).
Lt. Columbo is Italian-American, as was made a point of numerous times. Peter Falk is of Russian and Polish descent. Likewise, whereas Falk was Jewish, it was often hinted that Columbo is Catholic (at the very least, his own nephew's wedding is a traditional church-type wedding).
Hector Elizondo playing an Arabic national in "A Case of Immunity". Although Elizondo does arguably have the appropriate profile to fit such a person.
Jamie Lee Curtis had a brief cameo in season 5 as a waitress. Just earlier in that same season, Janet Leigh, her mother, played the killer.
It's also fun to play this with recurring actors throughout the movies. One person who plays either a random police officer or just a bystander in one episode might be the victim or accomplice in another. Sometimes, as with Dabney Coleman, a police officer in one and then the killer in another.
Both of the shrinks in Monk, Stanley Kamel and Hector Elizondo (Dr. Kroger and Dr. Bell). Elizondo was the murderous Suarian ambassador in "A Case of Immunity".
Kamel plays Tim, one of Congressman Paul Mackey's aides in "Agenda for Murder".
Patrick McGoohan (#6 from The Prisoner and Drake from Danger Man) appeared in four episodes over the series, all of which he was the murderer. He was also the director of all of these and two others — these got him two Emmy awards.
Little Richard cameos as himself in "Murder of a Rock Star".
This trope is played in-universe in "Uneasy Lies the Crown" when Columbo questions the poker players to the alibi of the killer — Nancy Walker, Dick Sargent and Ron Cey all portray themselves.
Non-Singing Voice: In "Murder of a Rock Star" actress Cheryl Paris plays the role of Marcy Edwards, the murder victim and former rock singer. "Closer", the song played in the episode was actually sung by Shera Danese, a frequent guest star of the series and Peter Falk's wife. Partly subverted as there was no actual dubbing involved, since we only hear the song played on stereos with no live performance. Weird, considering that Shera Danese was actually IN this episode, albeit as Trish Fairbanks.
Dick Van Dyke, who usually plays the comic relief in musicals like Mary Poppins or Chitty Chitty Bang Bang, as well as a comedy writer on the The Dick Van Dyke Show, played a particularly ruthless Murderer of the Week in one episode — a henpecked photographer who shoots his wife and a recently-released prisoner that he'd hired to run small errands, in an attempt to make it look as if the other man was the kidnapper.
Janet Leigh, perhaps most famous for playing the murder victim in Psycho, getting to play the killer in Forgotten Lady.
Bruce Kirby Jr. and Sr. in "By the Dawn's Early Light".
Peter Falk and Shera Danese. They were married shortly after her first appearance in the series and remained so until Falk's death.
Catherine McGoohan, Patrick McGoohan's daughter, plays the funeral home assistant opposite her father in "Ashes to Ashes".
Katey Sagal appeared in a small role in "Candidate for Crime", which was directed by her father, Boris.
Referenced By: A number of other shows have made shout outs to Columbo as well.
In Remington Steele a running joke has Remington referring to old movies to help him find clues to current cases. In one episode this is flipped, and his partner Laura Holt refers to TV series, specifically the first William ShatnerColumbo episode.
In an episode of Bosom Buddies, Henry dresses and acts like Columbo as part of a sting to catch a bad guy wronging Amy.
In an episode of The Odd Couple, Murray the Cop goes undercover to spy on Felix's ex-wife and dons a raincoat.
Murray: Whatta you think Oscar? Do I look like Columbo? Oscar: [You look] more like Dumbo.
Monk is also fond of taking things from Columbo. The episode "Mr. Monk and the Red-Headed Stranger" combines elements of at least four different Columbo episodes. Monk is also compared to Columbo on multiple occasions.
Clodumbo. In the '90s, they made him part of The ABC Misery Movie along with B.L. Strikeout and Giddyup Olive.
In Mad's parody of Star Trek: Voyager (starring Mrs. Columbo star Kate Mulgrew) Columbo can be seen in the background on one of the ship's monitors saying, "Take my wife, please!"
Throw It In: "Just one more thing..." In addition, many of Peter Falk's absent-minded moments were ad-libbed. He figured that if they were all scripted, it would be harder for his fellow cast members to react genuinely. So, in the middle of scenes with the suspect, Falk would unexpectedly start fumbling around for his shopping list or pretend to forget what he was talking about. The standard perp expression that seems to say "What is with this guy?" is thus usually very real.
Peter Falk wanted Patrick McGoohan to play the role of Findlay Crawford in "Murder with Too Many Notes", but McGoohan had acted in the previous Columbo film, "Ashes to Ashes", so McGoohan declined and the role went to Billy Connolly instead, with McGoohan directing (he also co-wrote the script).
Steven Bochco wrote the script to "Uneasy Lies the Crown" in 1973, which if it'd been made would've been a part of season 2 or 3. Peter Falk turned it down at the time, only to make it later in 1990. One has to wonder who would've been the killer if it'd been made in 1973.