It may be an artefact of your WP theme or another plugin doing something that only webkit recognises.
Can you give me a link to your site so I can see this? If I visit as a guest will I be able to open profile popups to look at one?

It’s a fresh WP install with no other plugins than SinglePress. The theme is Twenty Ten (tried with Twenty Eleven with the same result).

Here is the link. This is a test forum and currently Guests have Standart permissions so feel free to test around.

the unhelpful news is that using version 13 of Chrome on my Mac then I do not see any display issues at all. So can I assume this is restricted to Windows?

Quick check with Chrome under DamnSmall Linux shows no problem at all. So maybe is restricted only to Windows (in this case XP)

XP eh? Sorry but somehow not that surprised.
if you can use the Chrome developers tools you could examine the actual element being displayed there to try and determine the cause. That would also allow us to see if there is anything we could do as well.

The problem seems to be with the relative position for class .ui-dialog-titlebar. When removed the bar comes to the right place, but unfortunately without the close button 

My CSS knowledge is limited so this is the best i can do.

While testing around found something interesting – the problem is present only with maximized browser window. In scaled down window everything is just fine.

It seems to be problem only with my machine. Sorry for the lost time.

P.S. Sorry for the jagged screenshot, it was attached by mistake.

All most strange.
The popup (and the classes being used) are all using the jQuery Ui components which they usually do a pretty good job of testing so I am surprised at any odd behaviour to be honest.