Personally, I think it would be odd for an older ship that had just been operational to be having so many basic hardware and software issues.
Agreed. If Starfleet really was giving the crew such a gift for literally saving the planet, then I'd think it would have been at least checked out for problems first.
I suppose that makes about as much sense as anything else in STV. But if that were the case, then why did Admiral Harve send it out on a highly dangerous mission? Was he intentionally trying to get Kirk and his crew killed?
Well, the one piece of visual evidence we have is that at the end of STIV the Ent-A's bridge is the same type as the original refit, but in STV it's newer, implying at least some kind of major upgrade was done between the two movies and that it wasn't a new ship.