I tend to trust the film's internal clock and logic enough to dismiss any discrepancies as narrative choice. I can also see the "mistake" being a character-based one rather than a production one.
Negligible time difference between matches
The Barbosa fight is physically shorter, but the times between "bell" and KO for each match are negligible when one compares footplay against Barbosa with the pin-and-pummel on Mad Dog.
Arguably, the Barbosa call is unofficial; we only hear the commentator making a surprised, possibly hyperbolic claim as Tommy leaves the cage※. Also arguably, Tommy continues to pummel Mad Dog for several seconds beyond the knockout.
These seconds could make up the difference for what the commentator meant was the fastest technical/actual KO from match start.
Ambiguous audience perspective
Could it also be that the lengths of each match are slightly ambiguous to us, the audience?
We're once-removed spectators in the meta sense, watching a film about a fictional match built on a narrative rather than objectively seeing it in real-time in the real world.
The subjective view of a character may not be a mistake
"That's the fastest knockout I think I've ever experienced."
The commentator was surprised by the first KO and may not have accounted for time. By the third one he may just be tossing out a sound bite. It might be his mistaken view that Mad Dog's KO was the fastest he'd ever seen, distorted by adrenaline and the hype of a crowd that anticipates instant KOs, or he might be deliberately saying what he knows to be wrong to further discussion.
It seems likely in that setting, details of Tommy's victories would be enthusiastically debated by commentators and fans just for entertainment, regardless of the facts.
※ Technically, how legitimate is Tommy's win against Barbosa? Leaving the cage is an apparent rule violation in the film -- the commentator says so (audible but fading in the Youtube clip) -- but is not listed in MMA rules that I can find. I don't ask in order to complicate your question, but to point out that if the fastest KO comment is a mistake, so might be many other depictions of MMA that we previously assumed were narrative choices. If we accept those depictions as narrative choices, then it makes sense to accept the dialogue with it, as part of the film's internal logic. (Forgive me if leaving the cage is addressed in the intervening scenes of the full film, I haven't seen it for a while.)