Mix as you normally mix, just strip away anything that makes it sound "live" (i.e. crowd/audience tracks, editing or gating/expanding out noise or leakage). You may, in fact, have to convince them to re-record certain elements if they are deemed un-fixable or if the performance is lacking.

There may be plugins that you can use in the Waves Diamond Bundle (if your using protools) to help in improving the sound quality. Re-triggering the snare and kick drum may help as well.

This is all assuming that they were tracked in either PT, Nuendo, Digital Performer etc...

This is what I do most of the time, albeit recording bands live in the studio.

The same rules apply as with studio recording, trying to get the sound right to a certain extent before you go head. Obviously this isn't an option for you. But luckily, I think, there is so much mess and bleed that what you originally had isn't so important, you can get to the same end result every time.

I usually start with the kick and snare. I EQ most of the top off the kick, maybe a little click in the hi-mids, and use Waves TransX to give it power, ditto the snare in appropriate bands.

Bass is where you are gonna have most problems, its gonna come through everything, I usually DI and add Waves MaxxBass but you may have the opposite problem.

Guitars usually cut through well and have little bleed. Vocals you will have to see how the bleed is, I get amazing results with a 57beta in the live room, hardly any band sound.

Every track I compress using the presets on the Waves Renaissance compressor, and I use a tiny bit of room reverb on most tracks, with a decent plate on the vocals.

After that its just EQing the individual tracks to make them stand out as much as possible, and then multiband compressing and EQing the mix bus, which I find are fairly interlinked with the live stuff, you may have to overcompensate with one and draw back with the other to get the balance right.

Nothing out the ordinary and you won't get the band sounding like they were in a studio, obviously you know that, but you can get some kick-ass sounding recordings with the live energy, as long as the playing and onstage micing is good.

I don't know if this has been considered, but one thing I always like to attempt is a noise reduction. I use Adobe Audition (Cool Edit) and if I can get a good chunk of what is considered silence (for instance any low-level noise from tape or hardware) then I can make a filter and apply it to the whole waveform. It can make quite a difference just cutting out air conditioners and stuff like that, or especially tape hiss.
This is given the assumption that you're just wanting to clean up the recording, not redo the recording.
JJ

i use, filter, eq and even soundsoap in subtle settings to reduce the unwanted noise, and then a bit eq again to bring up a little the music, if used in subtle measurements, it works fine and i can reduce a lot of unwanted noise without destroying the musicality.

the standard plugins in audition are great. I use them for movie work where the location audio was...lacking. Just be careful with noise reduction and try out several different things with that plugin. It may take a while, but audition will do a lot.