In my case I have several sites in multi-site mode.
Site name is the same for all sites (domain name), so when I want to switch a site I have to shuffle thru all of them to get to the one I want. I got used to it after several months and I know where to point now, but still, it is hard to get directly to desired one if you have many sites with same site name.
Adding some kind of SiteNAME-tag would solve it.
Displaying site/path/ in the sites dropdown is my first thought... even ID number would be great.
Another thing is when Visiting selected site, I usually want to go directly to widgets or posts etc. and not to dashboard, so adding main links like settings, plugins, theme, posts, pages to the "selected" site dropwodn would be great...
Extended menu from Dashboard maybe?
Hope you find it useful.