Harry Potter
and the
Half-Blood Prince

The Cave

In the cave, Dumbledore detects various protections and deals with them. It seems to me that he could have given Harry better explanations of how he detected the protections and how he decided what to do about them. Harry didn't really learn anything about how he might be able to defeat the protections that might be present on other horcruxes — information that might really be useful in book 7. And he hasn't passed on any information on how to go about locating the other horcruxes.

Malfoy's Project

Draco Malfoy spends the whole book trying to fix the cabinet that pairs with the one at Borgin and Burkes, just so he could sneak some death-eaters into Hogwarts. Seems like he could have set up a portkey a whole lot more easily. We know that portkeys can be used to enter and leave Hogwarts. And they must not be all that difficult to set up — even the "ghosts" that leave Voldemort's wand in book 4 are able to set up a portkey to return Harry to Hogwarts (amazing how those ghosts were able to comprehend so quickly just how Harry had arrived there!).

The Prince's Book

Harry has hidden the Half-blood prince's book in the room of requirement. He is planning on not returning to Hogwarts (though that remains to be seen). Even though he now knows whose book it was, I can't believe that he wouldn't have gone back to retrieve it. It's got some very useful information in it.

Harry and Hogwarts

Harry is planning on not returning to Hogwarts. That seems like a very stupid decision to me. If he were to return, McGonagall would probably allow him access to Dumbledore's old office (presumably her office now). This would give him access to Dumbledore himself, via his portrait that will now grace the office walls along with those of other past headmasters. Harry can use all the help he can get!