I agree it could have been explained in a more believable way, but I also think the answer we need is in CaptainClown's post:
I'm not sure the cops knew there was a hostage situation, but they certainly knew that something was going down there AND that Gordon knew about it.
Think about it, they're setting a perimeter around the place and in a sec they'll come in and see Dent's body lying there. What can Gordon say? "Oh, I don't actually KNOW what happened, I just called you on a hunch and didn't really see anything myself, so... Yeah, unsolved murder, case closed"? Besides, it's very possible someone would see Bats leaving. I know normally he could just vanish, but here the police is right around the corner and he's badly injured. Not to mention any evidence that might suggest his presence there. The situation would at best be fishy, maybe tarnishing Dent's name (as mysterious death situations tend to do).
So, with the police knowing that Dent was dead there, that Gordon knew that something was going on, not to mention his family being there probably as hostages (he wouldn't just take them there for a family pic-nic, would he?) and possibly that Batman was there too, there are only two options available: blame Harvey or blame Bats.
Choose the second option, throw in the rest of Two-face's murders and you have a clean-cut case that makes Dent a hero and requires little investigation.
I, too, am usually VERY annoyed by plotholes, to the point that I just can't enjoy some otherwise well made films. But I think this case is relatively easily explained, even if it requires some thought.
P.S.: I know there' the question of why would Batman take Gordon's family as hostages, but I think an explanation could easily be thought of, or Gordon could simply say he has no idea why he'd do that.