Ascended Fanon: "Future Guy"'s name came from fans who started using it to refer to the humanoid figure and eventually, the producers of Enterprise used it as the character's actual name in the script. In his video review of "Broken Bow" years later, Chuck Sonnenburg commented how it pains him that what should have been the Big Bad of the series ended up taking a name derived from sarcasm, another sign of how the Temporal Cold War was poorly plotted and poorly planned. He was listed on the Memory Alpha wiki as "Future Guy" for a few years, before being renamed "Humanoid Figure" in keeping with the site's in-universe tone.
Jolene Blalock, a die-hard Trekkie from childhood, was the most dissatisfied - and vocal - member of the cast. Like Nimoy and Russ before her, she spent an enormous amount of time reiterating how true Vulcans are supposed to act and criticizing the scripts. She also found it a bit silly how T'Pol's hair never moves (if a single hair was out of place during a firefight, they would send her to makeup and reshoot it).
A lot of cast members were appalled at the series finale episode "These Are The Voyages...", which rather than allowing Enterprise to end on its own terms, turned it into a Star Trek: The Next Generation story. By all accounts no one liked this story, even co-writer Brannon Braga: Supposedly, Scott Bakula barked angrily at Braga over the phone when he got the script; Manny Coto was unhappy with how it completely glossed over the Federation-Romulan War with a Time Skip, and declared his own episode "Terra Prime" to be the true series finale; Connor Trineer was incredulous at dying such a lame death; Blalock stayed true to form by slamming the showrunners (again) for their meddling; and even Jonathan Frakes had his doubts about the whole thing. The fallout from the episode was so acrimonious that it negatively affected Braga's relationship with co-producer/writer Rick Berman, who described it as a "valentine" for Trek fans. Whoops.
Todd Douglass Jr.: I had to stop and think what Berman and Braga were thinking of when they wrote the episode, but I have a feeling it was after a late night filled with snickering and one of them saying, "The galaxy's not getting any of our bourbon".
Responsible for the much-loathed pop-song credits. Rick Berman is notorious for his milquetoast taste in music. This is what it would have looked like. If that music sounds familiar, it should — it's "Archer's Theme," the closing credits music, originally intended for the credits sequence and written by the same person responsible for Deep Space Nine's theme. An even earlier concept resembled the other Trek series' credits even more, including the famous Opening Narration.
Also responsible for the Temporal Cold War arc. The original idea was to have the first season based on Earth, but the execs nixed that idea and insisted that it be similar in tone to Voyager, and have a Time Travel element to make it "more futuristic." The execs then realized the TCW was going nowhere and demanded that it be removed, which is why it was abruptly finished in "Storm Front."
"E2" is often remembered for ripping off half a dozen episodes. What isn't too well-known is that the writer was specifically asked to make a number of edits for it to mimic previous ideas.
"Stigma" was part of a network-wide AIDS awareness anvil drop.
"Dear Doctor" was supposed to end with Archer and Phlox at odds with one another over giving a potential cure to the Valakian and Menk, with Archer wanting it and Phlox opposing it. But execs didn't want any disagreements between them, making Archer and Phlox both agree to not help, thereby likely condemning both races to extinction.
Fan Nickname: Future Guy for the guy in charge of the Cabal from the 29th century that was part of the Temporal Cold War arc. He was never given a real name on the show.
Follow the Leader: It can't be a coincidence that ENT's announcement came shortly before the much-anticipated second chapter of the prequel trilogy. This would explain the Palpatine-like hologram who bosses the Suliban around.
There exists an interview with Scott Bakula conducted in the run-up to the release of Star Trek: Nemesis in which he says, with utmost confidence, that the next Star Trek movie would be about him and his crew. Come 2008 (later delayed to 2009, but close enough), after what would have been the customary seven years, we did indeed get a new film - about Captain Kirk. Presumably, if either Nemesis or Enterprise - most likely both - hadn't bombed, we would have seen Captain Archer on the big screen instead.
Initial plans for the show that were changed before filming:
In very early stages of planning the show, the producers considered setting the entire first season on Earth and focusing on the lead-up to the mission, and only actually launching the Enterprise NX-01 in the season finale (which would make the title "Enterprise" a bit of a pun, in fact). There was an Executive Veto, and they were told to get exploring space from the start.
Mayweather was originally envisioned as older and more seasoned, making him a valuable advisor to the comparatively rookie Captain Archer. He was ultimately rewritten as green and desperate to prove himself, not unlike Wesley Crusher.
Plans for a fifth season, which was never made due to the show being cancelled:
The NX-01 would have been refitted with a secondary hull underneath the warp nacelles, ceramic plating, and a deflector dish, which makes it look very much like the prototype for what would become the Constitution in TOS. The new design appeared in the 2011 "Ships of the Line" calendar.
Shran would have become a main character and joined the NX-01 in an advisory capacity. Jeffrey Combs had been pushing to become a Trek regular since the eighties, and compared his perpetual b-status to watching a baseball game from the outfield.
Several reappearances of characters or species from the original series would have included the character Flint, the cloud city of Stratos, and the Kzinti from the animated series.
There would have been more stories set entirely in the Mirror Universe, following up on "In a Mirror, Darkly". They would have consisted of several standalone episodes interspersed throughout the season.
Tensions with the Romulans would have escalated, as a prelude to the forthcoming Earth-Romulan War.
More would have been revealed about T'Pol's father, specifically that he was a Romulan sleeper agent, leading up to the reveal that T'Pol was half-Romulan, explaining her inherent difficulties with emotion.
Peter Weller would have directed a few episodes, as part of the deal he made for his guest role in season four.
Mike Sussman's original idea for "E-Squared" would be the Columbia being thrown back in time instead—a result of trying to use Xindi vortex technology (likely salvaged from the crashed probe weapon). The NX-01 crew would thus meet the NX-02 crew's descendants.
Running the Asylum: Season Four alone has more explicit references to the original series then all previous Star Trek series combined. "In a Mirror, Darkly" restaged some events from a TOS episode frame by frame, also featuring a faithful reconstruction of a bridge similar to the original Enterprise.
This is also a rare case of this sort of thing dramatically improving the show on all fronts. Since the new staff really cared about making a good Trek show, they worked a lot harder at making the show good than previous teams had.
Word of Gay: Reed, to absolutely no one's surprise. The character is canonically straight, but fandom is more or less unified in believing that ENT's Armory Officer plays for the other team.