You really seem to have two complaints:

1) Technical issues (can't select seats in Chrome)
2) Usability issues (can't select seats post-purchase)

I generally haven't had issues using Chrome (my browser of choice). The only real issue I've ever had is that printing boarding passes via online check-in didn't work right, so I had to resort to using IE whenever I checked in. That particular issue seems to have been resolved a while back, though. I went through the process of booking a ticket today--using Chrome--and could select seats just fine. What build of Chrome are you on? I'm on 19.0.1084.46 (the current version). Also, are you on actual Chrome or are you using a Chromium browser, such as Rockmelt or Comodo Dragon? What OS are you using? I'm on Win 7 (Home Premium 64-bit).

Regarding usability issues, there are definitely things I don't like, such as clicking--which takes me to a different page entirely--, then having to enter my info on that second page, hitting the enter key, sitting there waiting a few seconds and then remembering I have to physically click the "Login" button with the mouse (that's ridiculous). That being said, the site is generally pretty functional (and the booking screens have gotten more attractive, recently, too).