The show has elements of this all the time, but there are also some that stand out, such as the occasional Running Gag of Harry and a guest marching around the desk accompanied by music and two versions of the Queen Vic bust from EastEnders.
Harry also likes to subvert or deconstruct this for humour — he will set up a BLAM, then try to carry on as though nothing had happened, but real life intervenes and elements from the BLAM keep interrupting him (such as actors involved in a BLAM sketch walking away behind him throughout the next segment as he tries to carry on).
Continuity Lockout: Yes, even on a sketch show. There are just so many Running Gags to keep track of. It doesn't help that, because of licensing issues with the clips from other programmes, it isn't available on any official catch-up services.
Crosses the Line Twice: Audiences have noted that there are several moments where Harry manages to get away with things that many comedians couldn't today, through the absurdity of his universe. Moments include cheering on Adolf Hitler of all people when he turned up in one of Harry's fights and joked about a character on EastEnders attempting to rape Pauline Fowler.
In series 3, Harry made fun of ex-footballer George Best's alcoholism, claiming his favourite foods were "red wine in a white wine sauce" and "ale and ale pie". After the TV Burp broadcast, Best died over a year later from kidney failure after relapsing.
Not long before her death, the show mocked Jane Goody's turn on Celebrity Wife Swap.
In the 5th season, Jimmy Savile makes a cameo in the Celebrity Big Brother house, receiving a cheer from all of the contestants, who gleefully take turns to hug him. This leads Harry to make his studio audience to make an impression of Savile's strange mannerisms when he presented his kids' show Jim'll Fix It.
In 2004, Harry included a sketch parodying the reality show 'The Real Mrs Robinson', which re-appeared in a 'Best Of' episode in 2009. Because they weren't named in the clip, no one on the production team realized that both contestants had died in the years since. Although OFCOM concluded that they weren't breaking any broadcast rules, ITV voluntarily removed the clip after complaints.
Hilarious in Hindsight: In the first episode of season 3, Harry joked that by 2006, Tony Blair would still be Prime Minister, Jordan and Peter Andre would have had their third child, and Pat from EastEnders would be back at law school. Hey, as Meatloaf once said, "Two out of three ain't bad".
Memetic Mutation: "There's only one way to find out...FIIIGGHHHT!" Self-parodied, to an extent, when said phrase was used in an episode of EastEnders in a conversation preceding a fight. Probably an intentional Shout-Out on the part of the 'Enders scriptwriters.
Unintentional Period Piece: Is to be expected if you ever get the chance to watch a rerun of the show. The series worked on reviewing many channel programmings of the time and the episodes that were on TV the week it aired; some of them have either stopped airing or in soap opera cases, many of the actors that Harry might focus on have either left, been killed off or died in real life. There's also a lot of mention of current news stories at the time and mentions of celebs that might have faded into obscurity, retired, or died as well.
Values Dissonance: A 2008 sketch parodying the documentary 'The Pregnant Man' involved Harry describing a transgender man as "a woman with a beard" (although he did otherwise refer to them as a he) and pretend to give birth himself while wearing a fake beard. In 2008, OFCOM didn't think this was offensive enough to break broadcast code (although there were complaints). This attitude had changed when (a toned down edit of) the same episode was repeated in 2016. UKTV note The repeat was on Dave agreed to remove the entire sketch from all future broadcasts.