I wouldn't go off of Zillow for home values. They are just ballpark. The tax value (and history of) is public knowledge at the County Courthouse, or at least here it is.
I'm not sure if you have/want children, but Utah also has as public knowledge a Sex Offender Registry - and ours is online. You put in an address and it gives you the registered offenders in the area, as well as their addresses.
Utah also has a site which every home listed with a realtor is posted. I would assume most states are like this as well. Ours is
www.utahrealestate.com for comparisons sake.
Also, you absolutely must do a home inspection. They are between 300 and 500 dollars here, and worth every damn penny. In fact, some lenders actually
require a home inspection.
EDIT: I would suggest you get a mold inspection as well, if it is not included in the home inspection. It's a pretty big deal around here as far as value is concerned. There is a house not too far from me that is getting gutted right now due to mold. It's is literally down to the frame all the way inside.
There is just one more thing that I wanted to add, and this is something I am adding to my checklist next time I buy a house. Recently there was a news story here about a couple who bought a house, and found that the previous owner had a meth lab operating inside. I'm not sure the exact details, but these guys could not move in until it was gutted. And they had just spent quite a bit of time and money remodeling the home. I'm going to look into testing for a meth lab on my next go around.