I'm no expert and don't have the CSS upgrade, but I did recently change my domains to the new dedicated url, and can set your mind at rest on a couple of points.
Firstly I should say that the process worked rapidly and entirely painlessly within WP.com. There is only one blog (just two domains), and there is no reformatting for you to do, or double-posting to keep up with, either.
That said, once the domain mapping was achieved, I found that there were a lot of minor housekeeping issues which I wanted to attend to. The redirects cover them all without problems, actually, but for the sake of accurate indexing of my site, I chose to update my various internal links and widgets (not least of these being the Technorati ones) to reflect my new domain address.
Since I have an index of pages which lists all of my posts by date, that took quite a bit of time.
I put up a post to advise people on the day of the change - in retrospect, I would better have done that one week before activating the domain mapping, but the re-direct works both ways, so it doesn't really matter.
I also chose to e-mail some key linked sites and regular commenters so that they would update their links to my new address. That takes people time to do.
My images all came across fine, and the image addresses do not seem change through the process as far as I can see. The file names all remained formatted along the lines of your_url.files.wordpress or your_url.files.wordpress anyway.
I changed the original feed address on my Feedburner account. Although the wording on their FAQ wasn't very good and actually seemed to advise against it, once I had carried that step out it worked immediately.
The Google listings on my site took several weeks to switch over and in part is till ongoing.
For a while, there were links to a mixture of different page url addresses, and in general, my posts fell way down or dropped off Google's results altogether. Finally, I verified my site with Google and I submitted an html sitemap, which seemed to help greatly, so that the page rankings are probably almost back to where they were now.
Nevertheless, six weeks on, the Technorati authority of my old address remains higher than my new one, and Google Blog Search has still not indexed many posts on my new url, although I have submitted the new domain a couple of times. They were all there one day last week, and then they mysteriously disappeared again. Such is the internet, I guess.
To summarise then:
time to change over url - 2 minutes
time to see url working - 1 hour
time to update fussy links, e-mail linked sites, adjust widgets etc - intermittently over 2 weeks
time to change Feedburner account - 2 minutes
time to Google verify site & submit sitemap - 30 minutes (tigredefogo's method is in these forums)
time for Google search results to readjust - 6 weeks, in part ongoing
time for Technorati ranking to recover - not yet
time for Google Blog Search to reindex - not yet.
The Technorati and Google issues perhaps take the longest to settle - and here I remember that engtech has written about how traffic concerns deter him from changing domains.
But provided you aren't too impatient, and have a little time to tie up a few loose ends, it's not too bad.
The stats all carry over seamlessly within WordPress.com, and I didn't detect any noticeable change in traffic beyond an influx last week of Liverpool fans zooming in on a post I had made about the 2005 Champions' League Final - hard to bear for a West Ham supporter like me ... *lol* ...
Good luck, then, and hoping that it all works smoothly for you.