Advice on hardware compressor
 

I have a Mackie mixer that I use for panel discussion, typically four microphones for panelists and a wireless handheld for moderator and Q&A.

I think it would greatly improve matters to have a hardware compressor/limiter, but for economy, I've been considering that on the mixer stereo output and not individual channel inputs.

What problems would might I be getting into here?

The only real problems would be if you had an expander turned on, and you had issues with low levels on some, and hot levels on others. In other words, don't expect a compressor to do everything for you. You'll very much need to set some levels, spend some time in set up. After doing so, the compressor is never a "bad"thing, as long as it's light. Remember that if you record with the compressor on, you're married to the compression. You can't "uncompress" audio.

24 bit has been mentioned a couple times in this thread. In my experience, the availability of 24 bit recording has greatly reduced the need for input compression when recording. 24 bit rules!

As a practical matter, the increased resolution means that when you set your peaks to a conservative -12db or -18db, and suddenly the band hits a quiet section that is now peaking at -28db, you still have lots of resolution, where with 16 bit I used to hear digital rez artifacts when I brought that -28db material up in post mix.