Is screen burn-in a problem? Screen burn-in can be a problem for older and cheaper monitors.  It can be caused by fixed-width text, fixed-size graphics, and operating for long durations, which are things that are common in aircraft displays.

So is burn-in a problem for aircraft? Have there been hardware or software improvements to minimize burn-in?
I was in the Regional Jet industry a long time and never heard of screen burn-in as a complaint on Rockwell Collins ProLine CRTs.  You mentioned "cheaper" monitors and that may be the key.  CRTs built to an aviation TSO (Technical Standards Order) are by no means cheap.