Since the modern Starfleet is no longer based on things like nationality, it makes no sense to exclude the aircraft carrier Enterprise just because its design predated the Federation.
Modern Trek repeatedly speaks of the pre-Federation era as one of barbarism. There would be a clear watershed there. And it just plain wouldn't make sense to include the (unknown!) number of previous holders of the name
Enterprise in the list of UFP Starfleet
Enterprises - the E-D is the fifth for that organization, even if she is the 76th or 85th or 327th (nobody can ever know the exact figure) overall.
In the TNG episode Frame of Mind a hand phaser set to its maximum setting and on wide beam could take out half a building, yet in DS9's The Siege of AR-558 everybody forgot this some what important fact.
That as such is not an error: real soldiers don't use the spray'n'pray setting of their assault rifles, because rationing of rounds is important, and so is aiming.
What is more serious is that Worf in "Chain of Command" actually uses Level 16, in blasting that little hole in that rock wall. Unless the rock was specifically difficult to blast, there would seem to be a discrepancy between the usage and Riker's claims. But of course, Riker would be fully entitled to a little bit of exaggeration in the situation he (thinks he) is in!
Then theres trilithium which goes from explosive starship warpdrive waste that everyone knows about in Starship Mine to Star destroying super compound that barely anyone knows about in Generations back to explosive starship warpdrive waste in The Chute.
"Barely anyone"? All we get in ST:GEN is Riker expressing a tiny bit of surprise at the claim that signs of trilithium were found on the observatory. He doesn't say he doesn't know what trilithium is and what it does. That his underlings nevertheless tell him (that is, tell us) is a routine storytelling device that hardly qualifies as a continuity error. Television and movie heroes are always muttering to themselves, stating the obvious, pausing dramatically and posing even more dramatically, and doing other such things that simply do not happen in reality.
As for the "phasers and warp coils in the 22nd century", people generally misunderstand what is being discussed in "A Matter of Time". Here's the real dialogue:
"Rasmussen": "What do you see as the most important example of progress in the last two hundred years?"
Riker: "I suppose the warp coil. Before there was warp drive, humans were confined to a single sector of the galaxy."
That's "progress", not "invention" or "introduction". Riker is really only claiming that warp drive made progress during those two centuries, and that he thinks this was the most important sort of progress made in his culture in that time.
Compare to Worf's choice:
Worf: "Phasers."
"Rasmussen": "I beg your pardon?"
Worf: "There were no phasers in the 22nd century."
Worf is clearly speaking of an invention. However, he's also speaking of progress made in the past 200 years, so it's perfectly acceptable to say that Worf is stating that phasers were invented during the latter decades of the 22nd century.
Trust me, if TPTB had deliberately retconned the Eugenics Wars to be in the 21st or 22nd Century, there would be dozens of people offering ridiculous explanations...
Of course. Why would anybody settle to saying that the (fictional) universe makes no sense, or is faulty? Universes cannot be faulty. They can only be poorly understood.
And it's pretty clear that TPTB didn't deliberately retcon anything there. There was no deliberate effort to move the Eugenics Wars forward in time, just a bit of careless writing or poorly researched pseudofacts.
As for TAS "Infinite Vulcan", it certainly doesn't state that the Eugenics Wars were 150 years prior to the ep. What it states is that the mad scientist who lived in the general period of the wars but was shunned (hence probably worked
after the wars, when there were stong anti-augment feelings) would be over 250 years old by the time of the episode - which makes possible any dating of the wars between late 20th century and McCoy's own time.
Timo Saloniemi