thesheep - 11:45 am on Jan 24, 2012 (gmt 0)
Note that it is sometimes quite reasonable for code not to validate, especially if using newer technologies such as bits of CSS3 and browser vendor-specific attributes, or bits of code included from Google Maps and the like who don't seem to be bothered to write valid code. But it's good to check there are no nesting errors, of course, and no old deprecated code.
If it's a small site, you could consider asking them to produce a responsive web design (RWD). Although in that case you might need to revisit your initial PSD design, as you'd need to consider the alternative (small screen) layouts right from the start, at the design phase.
But above all this, the main advice is: make sure it is well tested on all your target browsers! Ask them specifically to test it and give them a list of browsers it's got to look good on. They might use something like Browser Cam or similar. You could ask to see the screenshots too, for peace of mind.