Fake Brit: Whenever British people turn up, they always have Cockney accents. Even if they're the Gallagher brothers (from Manchester) or the Spice Girls (variously from Hertfordshire, Yorkshire and Merseyside).
Keep Circulating the Tapes: iTunes has made all the episodes of the revival and over a hundred fights from the original run available, but still, nearly half of the material from the first four seasons (including almost all of the commentary and storylines between the fights) can't be accessed legally. Fortunately, a lot of the stuff has been put back up on YouTube after Viacom's lawsuit against them failed.
To make things better, there are only three CDM tapes released (to this troper's knowledge): a supposedly "Greatest Hits" tape (consisting of 7 fights that are far from the show's "greatest hits"), and two compilation tapes (called "Celebrity Deathmatch: Round 1" and "Round Two").
McLeaned: Stacy Cornbred suffered from spontaneous human combustion after her voice actress left the show.
The Other Darrin: During the 2006-07 revival, Johnny Gomez, Nick Diamond, and Mills Lane were all recast. In Mills' case, he had a stroke, so he was no longer able to voice himself.