probably the most irritating thing is not having a "show new posts only" option (for logged in users). Or jump to 1st new post link. Wading through the waffle on here to get to page 3 of a discussion to pick up where you left off is pretty inefficient.
PM's not essential. Email notification not essential - but might be nice especially for threads you have started. The current system only works if you check it very regularly, and/or read every thread. Otherwise there are several pages of new threads. Which just get skimmed.
If I was the admin here - I think some photohosting would be the simplest/most important upgrade though; unless off site hosting is intentional to make it just inconvenient enough that people have to think about it. If I want to post a pic - I want to do it with one click not open a different window, upload it, copy the address over etc.
I'm not a fan of avatars, signatures etc - but those are not pre-requisites of a new format - they can all be turned off. I moderate another forum (vBulletin based) which has the default option almost as clean and simple as this - but which allows members to turn on showing avatars, etc for themselves if they wish - a privildge that they are required to pay for - which funds the site hosting etc.
I would say opening external links over the top of the current window is annoying and is not a great idea - as it makes people navigate away from the site. OK I can right click if I remember that this site is different from the 20 other sites I use from time to time.
Not refering to the original source of the quote is irritating - I often see a quote and want to see who said it, in what context, and if say it was a reply to something else. IMHO quote tools should include an automatic citation back to the source.
All the its free so who cares stuff? Just because something is free doesn't mean there can't be room for improvement. Its not totally free - I am being continually advertised to and buy STW so feel I am entitled to express an opinion on a forum intended to foster discussion. Most internet fora are free, at least for the basics, so why should it not be reasonable to suggest features that people believe add to the user experience.