When I start Kodi, the plasma panel freezes. When Kodi shuts down, everything goes back to normal. I'm on a dual monitor setup. I assume that Kodi is hijacking something while it's running, but google seems to be silent on the issue...

One other thing--the panel is functioning; if I click somewhere, it does as expected. It's just that the information on the bar isn't updated (clock doesn't change, window tabs don't update, etc)

Wow, this has been bothering me for YEARS, and I came up with the solution about 2 seconds after posting this.
The answer is to go to the system settings, and disable "suspend compositor for full screen windows".
Hope that helps someone else...

Well, that didn't quite do it. Whenever Kodi restarts or comes out of sleep, the panel freezes again. Actually, it seems to be a cached version of the panel; the clock always goes to 9:49 am. In the compositor settings, if I make any change and hit apply, everything is back to normal for a while.

to state the obvious cause of most problems - worth checking all kodi dependencies come from the same repository.

Well, kodi is running from the beta ppa. Many of the libraries are from the official ubuntu repos. However this behavior was the same when running the stable kodi version from the ubuntu repos as well.