As it came in Kubuntu, mplayer (with the gmplayer frontend) plays flv files fine, but the audio quickly gets desynchronized. After a while I can hear things happen a very noticeable time before they happen on video. This only happens with flash video files; avi, wmv, mpg... everything else plays fine.
Edit: I tested it some more, and it appears to have some trouble with long files too (say, anime episodes in mkv format). It's not nearly as noticeable as in even short flv ones, but it's there. Clearly something isn't right...

VLC plays flv fine, but I like mplayer's keyboard controls and superior startup speed and so wouldn't want to switch if at all possible.

I'd like to fix the audio issue, but I don't know how. Any help would be appreciated.

Have you tried uninstalling then reinstalling (hay sometimes it works)?

Isn't there options to delay or speed up the audio/video? There should be options for doing this, if not from the program, maybe from the command line.

This apparently will speed up the audio by 1.5x (not too much help to you I know but maybe it can be modified to do the opposite)

mplayer -speed 1.5 -af ladspa=tap_pitch:tap_pitch:0:-33:-90:0 foo.avi

this seams to be a problem with .flv files ,no matter what distro,

my smplayer GUI has the same issues
Use VLC

Try to use -framedrop option, it seems you computer is too slow to play strongly compressed videofiles.

well if the OP has the same issue as i then *.mp4 video play just fine, and *.rm are a bit hit-and-miss ( same as .flv) using mplayer