[trackercowe]

^ Some of those are problems, specifically the first two. I don't know why the issue with the Saboteur was never explained. Although the damage Kirk "fixed" by kicking the core happened when Khan shot at the ship, as Chekov fixed it prior to leaving their confrontation with Marcus.

As to your third point, Khan did command the ship to aim for San Francisco, so that's the reason why it crashed there. Also Khan was responsible for the ships construction, so maybe he knows how to build a ship that can sustain destruction from the atmosphere.

Also those weren't officers on Marcus' ship, those were just private contractors and mercenaries. Scotty said as much when he ran into one in the escape hatch (which was a poorly written exchange mind you). So they likely knew of Marcus' plan, and were in on it all along. Scotty was also on a ship that looked the exact same as the others around him, so he was able to sneak in that way. There were many similar shuttles around him, and I doubt they had the time to check them all individually in time to go after Khan.

As for your last point, yeah that's quite contrived, but I am sure McCoy did a bunch of tests, not just the one to see how it would react with a dead tribble. Once again it was such a damn obvious scene they practically beat its value over our heads, but I'm glad they didn't end up bothering with Kirk's resurrection in the next movie.