Where to begin, I have grown to love my old boat but maybe its because I've spent so much time fixing her up that I feel part of it. Don't get me wrong, she's fast, pretty and my wife likes her. A perfect mistress. So, if I was looking at a 34 today, this is what I would look for.
1. Check that the mast is not sinking into the boat. The mast support post tends to rot as it is a teak wrapped soft wood. It will be a little obvious as the deck will have a slight depression or there will be water stains perhaps near the top of the post.
2 Its an iron keel, check it for corrosion and rust. I just cleaned filled painted faired mine and its not cheap and not especially fun.
3 See if the forward stateroom door closes properly. I've read that flexing in heavy seas can distort the cabinetry so things don't fit quite right.
4 Make sure your surveyor brings along his snake inspection camera and have a look at the angle iron chainplate anchors buried in the stringers at the end of those stainless rod passing through the saloon.
5 If she has the original winches, they will probably be Maxwells which mechanically they may be okay, but they are small and with anything bigger than the stock headsail, I don't think they are big enough...plus the original winch handles may be long gone and the standard handles that fit every other winch on the planet will not fit properly. If you have the originals, they are gold. Don't lose them as Maxwell is out of the sheet winch game.
There are other things to look for and if you do a search on this site lots of them will come to light. Cheers and good luck.