TL,DR: The desktop version is just fine for mobile. Ensure that text reflows correctly on zoom. Use color for the comment tree. Make all links usable size. Fix chooser popup.
Long version: I like the desktop site a lot, and it works pretty well on my mobile phone.
I think that with just a couple tweaks, it would be excellent on small phone screens as well as larger tablet ones and desktops.
The only changes to the desktop site necessary to make it perfect for mobile, IMO, would be these:
One: Make sure the text always reflows properly when zooming. It is a huge pain to scroll left and right to read a line of text!
2: The lines at the left showing the comment tree, are unfollowable on a small screen, and thus waste space. Making them alternating colors would help a lot with deeply nested comments. Just follow the blue one up to find the parent, the grey one to the GP, etc. This would help on the desktop as well. Its hard to follow when you're 12 layers deep and there are a dozen identical vertical lines to try to visually differentiate. If we _must_ have only green, grey, and black on /. then instead use dashed, dotted, and solid lines.
C: When you get down deep, to something like a great-great grandchild comment, the lines of text have shrunk so much as to make clicking on a particular 'Re:' pretty hit or miss. Chrome mobile browser fixes this by popping up a magnified view of the click area when links are small and close together. A very convenient feature. Maybe /. could implement something similar. Or perhaps stagger the 'Re:' left and right a bit to separate them from each other. (Maybe not, messing with the indentation might send the code monkeys and Aspies among us into fits of homicidal rage)
IV: As many others have noted, the chooser popup is annoying and broken. You devs have seen and are fixing that, so, hooray and thank you.
Other than that, the desktop site is just dandy on mobile. I actually quite like it, and definitely prefer it to the big-text-children's-book-mobile-optimized-hot-messes that many sites offer.
Tweak the desktop version, and keep it unified.
One last problem I have been seeing for quite a while, with many different browsers, on my phone and on my laptop, is that part of a comment's text will be repeated and smashed onto the end of the comment. Like the following, but without the brackets.[mment's text will be repeated and smashed onto the end of the comment. Like the following, but without the brackets.]