Speaking realistically and with respect to wider Trek lore, nothing that happens after Kirk's trial could have happened the way it's shown. We've discussed the awkwardness of them getting from Earth to Vulcan in what couldn't have been more than 30 minutes at the most, but what about the journey back? Spock dumps Kirk off on Delta Vega (still a bloody stupid thing to call the planet) and then proceeds to the Laurentian system at warp factor 4. Assuming the Laurentian system is far away from the Vulcan sector, it's going to take the Enterprise a heck of a long time to get there, during which time the rest of the Federation fleet will probably fly past them.
Kirk wanders round for a while on Delta Vega before he runs into Spock Prime, then there's another passage of time before they meet Scotty and beam onto the Enterprise. Kirk assumes command, and then presumably orders the Enterprise to change course and head for Earth. Later Sulu informs Kirk that the Narada will arrive at Earth eight minutes ahead of them. Now the Narada had been at warp and heading for the Sol sector well before Enterprise and has a considerable headstart, so I should think Nero would have beaten the Enterprise by a bit more than a couple of minutes, unless during the voyage Scotty managed to upgrade the engines so that they went a little bit faster than the Narada, which I doubt is within even Scotty's capabilities. And we know Nero couldn't have taken the warp highway, otherwise he most likely would've already reached Earth and destroyed it by the time Kirk got back on board the Enterprise. And we still have the problem of why, despite its super-advanced technology, Starfleet is still no match for Nero. If all this new tech was designed with something like the Narada in mind (and especially if it was partially derived from it), you'd think they would do a better job. Ye god, what a shambles!!