I think you are making the cardinal sin of applying real-world science to Star Trek. Have you seen the amount of unholy interpretations of quantum singularities that have occured over the years?
You are also making some wild assumptions about the properties of the (completely invented) red matter. They quite clearly showed a mass of red matter particles bouncing around at the end, before they all combined and created a black hole. Seemed fairly clear that they were trying to say that lots of red matter causes bigger, more powerful black holes.
Trek has always been full of both good physics and dodgy physics. When dealing with invented substances, I think we have to assume that 23dr-24th century science is more advanced and our understanding is wrong.
Now if you wanted to criticise bad science in this film, I'm surprised you missed out calling them on the "supernova that threatened the whole galaxy." That one, I thought, was dumb. Particularly if you read the comics and they give greater detail on its behaviour. Add to the fact that creating a black hole on a supernova would have no effect on any material already jettisoned from the star.
If they'd simply named it something new (eg. a sub-space implosion wave or some such) it would have been more acceptable. But we've seen enough supernovae in the real world for the name to not really apply to this thing.
By "engine" I assume you actually mean the warp core. Well, technically, they would have been more out-of-sync with continuity if we had seen a warp core in this film. There never was one in TOS. We could see though to (a matte painting of) an array of injectors or some such devices. In fact, there is a cursory resemblance to the array of tubes we saw Scotty ejecting the core from in this latest film.
As for the engine being a particle accelerator - not really. Its always been a matter/antimatter reaction chamber - where streams of deuterium and anti-deuterium are safely combined by way fo the dilithium crystals, converted into a high-energy plasma and channeled off to the nacelles. Let's be fair - a device like that could lok like whatever you want.
Well, its an assumption either way as to whether they knew about it or not. You could also complain that they were using the TNG-era UFP flag aswell. But I also thought that was clearly because the TNG-era one looks better.
They used the delta symbol on the Starfleet badge on Enterprise, too. Its not as obvious, because its a part of a more detailed patch (and we don't see much of Starfleet throughout Enterprise, either) but it is there.
Heck, perhaps Starfleet adopted the "different emblems for each ship" AFTER this point, then switched back to having the delta symbol for the whole fleet when their designeers failed to come up with decent logos for each ship. There you go - continuity problem solved!
Don't forget the peace negotiations over sub-space radio from the Earth-Romulan wars. That should provide enough detail for Uhura to have learned the language. Let's face it, you've got to assume Starfleet Intelligence would have been keeping tabs on Romulan communication ever since that war.
Let's face it, all Uhura had to do was spend a few hours a night playing with a universal translator and it could have worked out all three dialects without ever having heard the language before (becuase they do that!)
Well the point is that they would have upset a whole lot more people if they had gone with a full reboot. So they took an approach that would - hopefully - meet both sides in the middle.
I honestly don't think this was done to get out of doing research, though. I think it was done to avoid getting bogged down in 40 years of continuity. I read an interview with Trek-Veteran (and new-BSG head) Ron Moore, in which he said how difficult it was getting to write for Star Trek, as it got bogged down under its own continuity.
Just look at how much flak the writers of Enterprise got whenever they bent continuity even slightly. I'd say this "alternate universe" idea was simply a way out of that. Not to avoid research, but to avoid having every little detail critiqued. Whilst you or I might be willing to overlook minor continuity errors for the sake of a good story, the fandom as a whole clearly could not. And it was killing Trek.
However, I do agree it would have been nice to see a straight origin story for TOS - particularly because its the only one of the series that's never had one. I also really liked Captain Pike in this movie and I think it would have been nice to have him remain as Captain a bit longer.
