The H34 model years are 1983-1987.
I disagree with the fact that these have a hard time in light air. We sail an H34 in the Chesapeake and it does quite well in light air. Big rig and lots of sail. You have to reef it early since there is so much sail and it is a little tippy, but good light air boat. Not built like a Hinkley, but a heck of a lot cheaper. Very roomy and good layout. It is a ton of boat for the money - you will not find a bigger 34 footer of the same vintage for a better bang for your buck value.
There are some common problem areas to look for when looking at these (like any model of boat). Some of the major ones are the compression post, leaky window ports (common of a lot of boats), etc. Look at
www.hunterowners.com at the H34 under owner reviews and you will see lots of information. Post there and you will get a lot of feedback on this model. Good luck.