Same here for Practice mode since last week. It started happening suddenly, while I was on the quakelive site.
I had played in practice mode earlier, then switched to the online page. Was sitting there for an hour or so, while doing other things. Then when I click on Practice, it started to display the page, then froze - and it's been freezing ever since, whenever I click on Practice.
I have tried removing Quakelive completely and re-downloading everything from scratch, but to no avail. Practice just stopped working mid-day.
Wireshark snooping says that it downloads the image files for the game types before it froze.
Firefox profiling says it froze in "compiled_v2013071600.0.js", line 709, in function:
done() (line 17)
module.ShowContent() (line 709)
PreparePanelHandlers() (line 709)
<Anonymous>() (line 709)