Is the theme responsive?
That is, will it also work on an iPad or other tablet, and an iPhone, Android or other smart phone?
Should you use a framework like StudioPress Genesis, Pagelines or WooThemes? Keep in mind you’ll be married to that framework, and any quirks that come along with it. Many developers have a preference, or prefer using themes without the framework [that's me, usually! As always, depends on what you're doing!].
Create a child theme, so the original theme can be updated and left untouched—your changes are kept and your theme’s vulnerabilities are fixed in its next update.
Free is not better. There are good free themes out there [the WP theme library has a lot, but of course most of those looks like blogs], but when I recently worked with a big brand who relied on a free theme, I spent more time fixing hacks on an abandoned template that didn’t keep up with WP upgrades. Talk about a pain!
SEO: Don’t rely on the theme being called “SEO friendly” as being enough. Good search engine optimization requires each page or post being optimized.
Does the theme have everything you want out of the box? That is, if you want social media icons at the top, it may not be simple to make this happen, and may require extensive hacking, depending on how the theme was built. Get as close to all of the features you’d like off the bat.
Special control panels can be a pain. Many developers offer these “easy” panels to ease customization, but this sometimes buries or obscures code.
Don’t expect the theme to install just like the demo, with everything working, out of the box. In fact, be prepared for more of a mess! Many themes these days have custom post types, designate posts and pages for different things, and usually have a lot of quirks that may not be explained, even in paid themes.
Is there a support forum, and how fast does the developer respond? Are there support queries sitting out there for weeks or months? Support forums are the lifeblood of WordPress, since someone else has likely encountered the same problem and can help quickly, but not all theme developers are available at a moment’s notice.
Don’t keep the exact look of the theme — chances are others have, and you don’t want your site to be a clone of the dog walking business down the street!
Keep a WordPress guru on hand [yes, I'm emailable!], because you’ll need advice, or more likely, someone to come in and clean up the installation and make things work as they should. Many of us are in WP all day long, so that issue that takes you 4 hours might just take us 15 minutes!