Some of this is not directly related to accessibility but found during testing - if it isn't suitable here let me know and I'll repost other bits elsewhere.
This is just a quick front end test, I'll work on the back end another time.
All tested with the default theme.
divitis, some of these should be <p> not <div> eg.
<div id="pun-title">
<div><strong>beta beta</strong></div>
</div>
<div id="pun-desc">
<div>punbb access</div>
</div>
the inner div's could easily be a <p>
I realise that as many hooks have to be put in as possible, but if the number of div's can be cut down it may help. (yes I know it is probably themeable)
The skip link, even works in IE7 (haven't tried in earlier versions)
In table markup I see use of: scope="col" this isn't as good as utilising headers and ids, more difficult to code, but may be more suitable.
Default last post link text - eg.Today 10:59:23 it doesn't really describe what it is linking to (but you can easily argue 'it should be bloddy obvious on a forum') however there may be some times when the link text is not unique, and therefore you might get 2 links pointing to different places but with the same dats and time - which would make this unsuitable. Sorry I haven't got a suggestion at this time to fix it.
Suggestion re links - if underlined remove underline on hover(and active etc), if not underlined, add underline on hover(and active etc). This does happen in some places, but not all. eg breadcrumb
Quick post form,
<em class="req-text">(Required)</em> if that text isn't in the <label> then screenreaders who have gone into forms mode won't be able to 'hear' it. However I do notice the workaround on post.php, but it wasn't implemented here.
Profile section : avatar
sounds like a silly question but why is it 'required' when surely it is optional?
search result - suggestion, add an id(#searchresults) and send the user straight to the results, rather than forcing someone to tab through (or even scroll down).
If anything needs explaining further or expanding on, feel free to ask and I'll do my best to answer them.