It looks like for some reason that it's unable to load certain elements. The first appears like it was simply unable to load a few images. The second looks like it was also unable to load some stylesheets.
My guess would be that Firefox is unable to open network connections on occasion. The two things that come to mind that might be causing that are firewall/router limits and OS limits.
Honestly, I feel like OS limits are more likely. When you see this happen, try this: Open a Terminal and find Firefox's process id:
% ps ax | grep -i firefox
13120 ?? Ss 253:53.47 /Applications/Firefox.app/Contents/MacOS/firefox-bin -foreground
16336 s000 R+ 0:00.00 grep -i firefox
That shows that Firefox's process id is 13120. Now see how many filehandles it has open:
% /usr/sbin/lsof -p 13120
COMMAND PID USER FD TYPE DEVICE SIZE/OFF NODE NAME
firefox-b 13120 wfaulk cwd DIR 14,2 1632 3269319 /Applications/Firefox.app/Contents/MacOS
firefox-b 13120 wfaulk txt REG 14,2 34220 7858208 /Applications/Firefox.app/Contents/MacOS/firefox-bin
...
firefox-b 13120 wfaulk 97r REG 14,2 8599 3527761 /Library/Internet Plug-Ins/Flash Player.plugin/Contents/Resources/Flash Player.rsrc
firefox-b 13120 wfaulk 98r REG 14,2 286 3527759 /Library/Internet Plug-Ins/Flash Player.plugin/Contents/Resources/English.lproj/Localized.rsrc
Count the number of rows that have a number in the fourth column, regardless of a trailing letter. If it's close to an even binary number (that is, 128, 256, 512, 1024), process limits might be the problem.
Does it only happen after Firefox has been open a while? It might be leaking file descriptors for some reason, probably due to an extension.
That's enough to try initially, I guess. Get back to us.