I've worked in this same situation before as well, only we used fewer mics (8 or 10) and swapped them between about 20 performers. It sounds like you have enough mics not to swap them between performers? That can make things easier.

What sort of mics are you using?
If they are wireless, make sure that they all play nice with eachother. It can be difficult to find enough open and interference free radio channels with that many mics.
Are they handheld, lapel, or headworn? Depending on how many mics you have open at one time, feedback can be a big problem, ESPECIALLY if using lapel mics.

• Make sure everyone ALWAYS uses the same mic each time.
• Use some masking tape to label the board.
• Get a script and write notes (LOTS of 'em!) on each scene or cue about what mics to turn on or off.
• Have a helper sit with you. They can follow along in the script and flip pages and whisper in your ear. So you can keep your eyes on the stage and mixer while they follow along in the script and give you cues.
• If you can, try to group your mic channels so that most in-use mics are close to each other or next to each other during a scene.
• I like to put the most used mics (usually the main characters or main performers) on the left side of the mixer, beginning with channel one, just to make them quick and easy to access.
• Adjust gains so that each fader is close to unity (0 dB) during the performance. This gives you a good starting point when "un-muting" the channel, making it easier and quicker to do so.
• Unless you have a separate monitor console and operator, minimize the use of vocals in the monitor mix. In most plays and musicals, I only put the accompaniment tacks or piano in the monitor mix. This is even more important if you don't have a mute button on your mixer.
• Have a spare microphone or two ready backstage. Educate everyone to know the purpose of the spares. If a mic has problems, they should grab the spare and use it.
• Have a stagehand backstage that knows what to do in an emergency (like get the spare).

IMO, it all comes down to LOTS OF PLANNING and a bunch of practice. A good script should allow you to know what mics to turn on and off at the right time without even watching... just listening and following along.

If something goes wrong, have some contingency plans in place.
If something does go wrong, don't be afraid of interrupting the performance. I find that the audience is usually more appreciative if you stop and work things out instead of let the show go on and pretend nothing is wrong.