You should always sign up for Google Webmaster Tools and whatever MS has, Bing Webmaster something. Yahoo Site Explorer is dead or dying. Everything can look great but not much use if bots can only see half the site - for whatever weird reason. Also quite a bit of SEO related info there.
Might be stating the obvious but when you see "Clean code" attached to a theme it only means that a default out the box setup is clean. Once you add content and plugins, perhaps via plugins, hell can break lose. Selecting best plugins is the trick - and theme of course. And what Renegade said about markups.
For SEO plugin some are more useful than others but I think this is cool Wordpress SEO Plugin http://yoast.com/wordpress/seo/
by a WP-guru who can afford to share
Notice the almost official title, he know this will be popular. His name Yoast is almost a brand. Site has most SEO info a normal person needs to know btw. Plugin like his is what people use if not theme is "SEO ready". I especially like snippet preview, don't think many pay attention to that. Is what people see in search engine so important. You do it already but may be not optimal for the end user experience - and willingness to click, click.
SEO ready means some features, not all, of a typical SEO plugin are build in the editor page. So you can attach meta tags for example, change title. 8There will be more like how theme loads css, js. easy way of attaching Google Analytics/Adsense code and what not. More important is you use something that is updated and supported, not likely to go out of business any time soon. Now WP 3.1 is close, so does all your handpicked stuff work, will it be fixed/updated? Quality more valuable than pretty colors of course. Can always use plugins, not must have feature. Actually I don't know what SEO ready means but this covers some of it. Can be whatever, "optimized code" is also an SEO feature if that means speed.
Does not really matter if theme is SEO ready or not because it can be dumb to use theme for this. If you later change theme all info is most likely gone, seo content is in themes datatables. The plugin I mentioned has import functions for this reason, one of the first with this I think. May be there is one which let you import/export among the most popular tools, don't remember. But some have learned the hard way, as in strange drops at Google = game over! If plugin is used theme SEO-stuff must be disabled and the other way around.
Checking all what has been mentioned about alt, meta something is easy with SEO-doctor http://www.prelovac....er-addons/seo-doctor
real-time and by another (smaller) guru. They know how to build a business those 2
Firebug + extensions for Firebug, Google Page Speed http://code.google.com/speed/page-speed/
can do the same and more. Select right tools with "Don't waste my time, I do not think it is that interesting, thank you!" as one of the parameters and there is close to no work involved. If you always forget to use alt info for image then just install a plugin which does it automatically, like SEO Friendly Images http://www.prelovac..../seo-friendly-images
As Renegade said most is simply technical things any site admin should know anyway, Google Webmaster pretty much cover what is important as far as technical SEO goes. Not much need for extras but you could be missing out! Can be difficult to select but go after popularity and check homepage, some are made by pros and even WP employees. Others by 16 year olds with more ambition than experience. You can tell. They don't review pluigins that closely, just poor them out so it is a supermarket. Close to 13000 to pick from. Lots of buggy outdated stuff and potential for conflicts with both themes and other plugins. Where it can go wrong, look at any WP forum - once you start tinkering door is wide open for "problems". KISS principle apply here as well. Less is often better with WP. Not always easy to remember when it stinks so much with some features
Still true, the more you add the more you must know and to some degree maintain.
If you want max. number of visitors fastest way possible I suggest pixel boobs not SEO.