It always comes in slightly to the side of the barge and as part of the landing burn it does a final sideways correction. I believe it was for this kind of situation - or one where the final burn doesn't even happen.

I read somewhere that the drone ship was damaged.

Elon mentioned in the press conference that two of the engines on the droneship (it has four, one on each corner) were damaged.

Do they send another ship to fix the drone ship?

There's another ship nearby which tows it, it doesn't go all the way in and out of port on its own power.

And the ship has taken far bigger poundings in the past, one of them blew a huge hole in the deck.

Oh ok, cool. I guess I thought it was more autonomous than that by the name.

Watching the other boosters land was really impressive.

I think it's just fuel saving for the ship rather than lack of autonomy

More time than fuel I think. The droneship has precision-manoeuvring thrusters, not engines that would let it move at any significant speed.