Characters in Star Trek have certainly screwed up before. In Enterprise alone half the premise is pretty much predicated on everyone screwing up at one point or another as they try to figure out how to set the standards established as a matter of course in other incarnations.
But "Cogenitor" is probably the be-all-and-end-all of screw-ups. Naturally it features second-half-of-the-second-season-all-star Trip Tucker, in the episode that solidifies that role. It's the last time in the series, actually, where one of Trip's spotlights does not focus on something about him other than his personality and apparent bad instincts, probably because the writers no longer have any doubt after it that he's the breakout star of the series.
Before we get to that, let's just get out of the way another of Enterprise's efforts to make a franchise reprise of some of its most notable actors. This time it's Andreas Katsulas, who famously played Picard's Romulan counterpart Tomalak (although he's better known as G'Kar in Babylon 5). He gets to spend a lot of genial time with Archer in a first contact situation that's one of the best this crew has experienced.
Except for Trip's actions.
Several times in the course of the series alien species truly get to be alien, meaning that they have noticeable characteristics other than their appearance that makes them alien. While it's happened in other incarnations, there's a more pronounced effort in Enterprise, even if it happens in an alien-of-the-week context most of the time. Here it's a species that has three distinct genders. Trip gets his knickers in a bind when he decides for himself that the third one is being unfairly exploited and limited in its potential. He meets a couple who are trying to conceive, and so they have one of the eponymous members of this gender accompanying them. He becomes intrigued by this individual.
And he screws up big time. You can imagine what happens next. Riker did basically the same thing in "The Outcast," but where that episode used Riker in a fairly uncomfortable representation of his latent Kirk ladies man mode, Trip is Trip in "Cogenitor," a fallible human who probably thinks too much for his own good, the version of Archer who would've made the Vulcans even more uncomfortable (but who is ironically revealed to help the future captain get his father's engine working in "First Flight" two episodes later). He's everything that Enterprise was supposed to be, and gets to be it for four seasons, warts and all.
Whereas most episodes like this end up being about the issues they were engineered to explore, "Cogenitor" is best viewed for its featured character, and that's the true strength of Trip, that he could make something like that happen. That's how he gets one of his bona fide Star Trek classic episodes.
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Memory Alpha summary.