“I have a mostly digital studio where everything is at 24-bit, except I have one reverb that is only capable of 16-bit audio. I’d like to connect it to the 24-bit mixer, but I don’t know what kinds of problems that could cause.”
You can connect it like you’d expect and it shouldn’t cause any problems per se. Your 24-bit mixer will send a 24-bit signal to the reverb. At that point the 8 least significant bits (LSB) will be truncated off of the signal and it will then pass into the reverb as the16-bit signal that remains. The reverb will output its 16-bit signal, which will return to the mixer where it will be read as a 24-bit word. This new 24-bit word signal in the mixer will have only 16 bits of valid (meaningful) data – the most significant bits (MSB). The equipment takes care of the bit depth discrepancy in sort of a brute force method, as you can see.
The biggest problem with this scenario is the truncation that occurs going into the reverb. This is not a great way to get from 24 bits down to 16. If your mixer had the ability to dither the signal down to 16 bits you’d be better off. Sometimes we get too obsessed with running things digitally. In some situations better overall sound quality results from just using the analog connections. You’ll have to experiment with your equipment to see which method yields better results sonically. Since we’re talking about a reverb here (presumably connected in an effects send and return configuration) it may not be that big of a deal either way. If, on the other hand, we were talking about something like a compressor that was to be inserted on the whole mix, I would be much more concerned about either of these methods, and would probably opt for a high quality A/D and D/A converter setup in between.