-The Borg are all one mind and one personality - and that one mind and personality is the Queen's. Think Deus Ex: Invisible War's hivemind ending, with the Queen as Alex Denton.
-Thousands of years ago the Borg spread their (biological) species to primitive areas of space, as an experiment on social development or whatever. This is why Kirk's Enterprise encounters so many crazy human worlds, why the Borg all look like humans, why the Borg haven't taken out the Federation, why the Borg seem so focused on Earth, and not the rest of the Federation, and why they don't just swat down Voyager like the pest Janeway is. It's all just collecting data. V'ger was the same deal - just a test on their lab rats.
-The reason no one knows about the Borg in TNG, despite Archer finding them? It was just filed away in the "weird one-off crap Enterprise encountered" file, which was only really studied by historians and particularly nerdy high-school students.
-The Illuminati, Masons, whatever, were real, keeping true technology levels hidden from the general public, among other things. The several factions fought their wars through small proxy conflicts; Kahn and his group were one of them, but they got ousted somehow and fled in their sleeper ship. Things went down hill, etc, the public found out little by little, and eventually it led to WWIII. The high tech levels were why the Vulcans kept checking on Earth every so often, and why Cochrane was able to build a highly advanced warp engine in a post-apocalyptic world at some dumpy missile silo in Montana.
-The Daedalus class was the first ship designed by Federation engineers, combining the knowledge of the various founding races.
-Because of the needs and physiology of the several species in the Federation, design philosophies of the early-mid 23rd century were severely minimalist, with unlabeled lighted buttons and switches dominating (flat touchscreens were not favored by Telarites, or whatever). As other species joined the Federation, the switch to easily-modifiable (in both layout and spectrum) displays and controls became more used, until the LCARS was developed.
-The Scimitar was a top-secret Romulan Doomsday weapon, developed by the Tal Shiar, built in some of the spent dilithium mines of Remus to hide it from the Senate. Because of the secrecy, they didn't post enough guards over the Reman laborers, and they were able to take over the ship, having to be led by Not-Picard since they were a bunch of know-nothing, pretty dumb Remans.
-Trip didn't die as seen in Riker's holodeck program. Trip actually had his own command at that point. The Enterprise's engineer did die, but history remembers Trip as the Enterprise's engineer, so that's what Troi remembers when she made the program to help counsel people.
-STO is canon, in its basic form and story. The ships are all canon, and came from the time period they look like they're from. There are even a few refit-Connies still running around - none of the acutally refitted original Connies, but the new ones built at that time period. The Excelsior-class took over flagship duties, but the Connies remained in service, eventually replaced by the Vesper class, but still sticking around like the Mirandas despite that. (Some of the remaining Connies were upgraded to the Exeter class during the Dominion War, to be able to actually possibly survive (the Mirandas were manuverable enough that they had a chance), but they weren't finished in time to take part in the conflict).
-The Enterprise-A was the Yorktown, which was badly damaged doing something shortly before TWoK and was actually decommissioned rather than get repaired - there were new Connies being built, and they didn't need the old ship; it was only being repaired enough to be put in mothballs. However, the Enterprise was destroyed, and Kirk saved the Earth, so Starfleet decided to reward him with a new one; however, the only Connie around was the decommed Yorktown, so they just gave it a quick paint job after Spacedock got back up and running. That's why it was in such bad shape in STV.
-The Intrepid class was the fastest in Starfleet at the time. They were even fast enough to escape from Dominion patrols, so they were mainly used for scouting missions, VIP transport, and other sensitive duties, which explains why we never see them in fleet battles.