Craig Ferguson was an alcoholic through the 1980s, and only got into rehab on the good word of one of his comedian friends. Due to his first-hand experience with addiction, he won't make jokes about people showing signs of substance abuse.
Executive Meddling: A glaring example. In his Doctor Who tribute episode on November 16, 2010 (his main guest was Matt Smith), Craig planned a Cold Opening dance number where he would sing his own lyrics to the Doctor Who theme music while his back-up players and puppets dance around (one, Michael Clarke Duncan, a big African-American guy, even sporting a Tom Baker scarf). Five minutes before airtime, CBS received word that they couldn't use the theme music because they hadn't been able to clear the rights from the publishers. Here's the original cold opening, complete with Matt Smith cameo at the end... and here's the open they ended up using. It is sometimes said The BBC was responsible for this, but this is not true, as the rights to the theme music are held by a publisher, not the BBC (a similar licensing issue nearly resulted in the 1996 TV movie having to replace the theme music).
Fan Community Nicknames: Craig himself uses "hobos" for his studio audience, and "robot skeleton army" for his Twitter followers.
Keep Circulating the Tapes: It's not out on DVD, since David Letterman apparently believes repeats hurt the value of the first-run episodes of his shows, but most (if not all) episodes since 2009 are floating around YouTube right now. Neither Craig or CBS really seem to mind, mainly since A) it gets Craig more international exposure, B) there's no annoying unskippable ads every few minutes, and C) there's no commercials period.
The Craig fans were hit hard in early 2010 when Malinky2Stoatir, probably the most well-known uploader of Late Late Show episodes (and a gigantic Craig fan herself, not to mention a very similar sense of humor) — whose uploads were watched by tens of thousands of subscribers around the world — had her account pulled down by YouTube. She quickly returned with a new account called "TVsCraigFerguson" and continued uploading new episodes (along with classics from the old channel) until it was hacked, at which point she moved to TVsCraigFerguson2.
While the show itself hasn't directly mentioned Malinky and her work, it's pretty obvious that they know about her: for one, she has a Twitter account, and one of her 5,000+ followers is none other than Craig himself.
One of Us: Craig has fully accepted his status as a Whovian, much to the rejoicing of Whovians across the world. He has also been on the Nerdist podcast, and The Late Late Show is generally considered the late-night show for nerds.
He also mentions his Whovian status in the Stan Lee interview (see the Funny Moments tab).
Craig: I'm not even a proper fanboy, because the people who go to Comic-Con — they all know about stuff. I'm like "Huh, Doctor Who's cool!" and they're like "Oh, which Doctor, loser?" and I'm like "I don't know!" You see what I'm saying?
An email segment in November 2007 included a letter asking for baby names. Craig, admitting it as being "the only name I know", suggested...Susan.
The Big Bang Theory crossover sketch had Craig state facts about Doctor Who after he fails, trying to impress the group...although he mistakenly refers to the main character as "Doctor Who", which would hit the Fandom Berserk Button of many Who fan forums.
He even gets in an argument with Chris Hardwick about whether the Doctor is a superhero.
Craig: He wasn't sent to Earth, he came of his own accord. Superman was sent to Earth, Doctor Who wasn't sent to Earth. He came of his own accord. I think there's a difference.
No Budget: Craig has mentioned in several interviews that he can't do all the comedy bits he wants because the show's budget is extremely limited. Of course, being Craig he constantly picks on the minuscule budget during the show.
The only reason the show has multiple puppets is because they bought one and the producer was so happy they were on TV they sent several others.
He also points to the lack of budget as to why he doesn't have a house band, like other late-night shows. However, a running gag started in late 2013 promotes the new house band 'Alfredo Sauce and The Shy Fellas', which is really Thompson doing voices mixed with stock-music big-band fanfares, with the idea the band is behind the stage curtain that the show uses for the occasional musical guest or standup act, and doesn't want to be seen.
The Other Darrin: Impersonator Josh Robert Thompson took over the role of Geoff from Craig after the character's first week on the show.
The Other Marty: Thompson himself was replaced from November 7-21, 2011 due to unavailability. Many well known actors and personalities like Alfred Molina, Larry King, and Thomas Lennon (Who turned Geoff into Khloe Banderas) were used in his place. Lennon again replaced Thompson between November 28-30, 2011.
Geoff Peterson's mouth and arms have stopped working more than once. They just kept on going, with Craig claiming that Geoff was communicating telepathically. In another memorable incident, Geoff's right hand popped out in the middle of a show.