Well, to be honest I can't see how an upgrade would suddenly have made all those errors appear, I really can't.
However, the upgrade might have caused an issue with one of your plugins which happens to have knocked things out of kilter in IE7 (you should see it in IE8beta2 - it's even worse!).
However, when you've got a whole host of issues like that, the best thing is to slowly pick through your template file and fix each of these issues.
If you're using Firefox I highly recommend Firebug and HTML Validator to speed up the tracking down of these issues.
I think your biggest issue probably arises from a missing
</div> as this sort of thing can cause havoc with style and layout!
I'm kind of amazed that it's rendering right in FF3.
The only other thing to check out is to go through your plugins and turn them off one at a time and see if it makes a difference.
And one other thing that occurred to me is to remove the text widget from your sidebar, as the issue seems to be coming from there on in.
It is possible that the text widget in 2.6.5 has a typo and is missing a
</div>. If that does fix it I will have to eat my words about it being highly unlikely that an update would cause this ;)