I've had this happen at least a couple times a week and I"m totally stock. I've also had it go crazy and start jumping around. I've also seen it go to straight blue screen. Like you, I turn off and back on the screen and it's fine. I figure I'll be told to wipe the phone and I'm not interested in that.
I also have these issues (split screen, blue screen, etc.). It first presented itself about a week after I got it, on Thanksgiving no less. For the most part it happened pretty intermittently, like once every week to 2 weeks, so I didn't really see the need to resolve it. I had to do a factory reset (for another issue) about a couple months ago. It did not resolve the issue. I contacted HTC about it and they said they would look into it. A few days later I got an email about possible solutions. They were to recalibrate the G-sensor, do a soft reset (pull the battery for at least a minute), & check and see if a task killer was installed and behaving erratically. No help with any of their suggestions. Around that time I actually had it happen three days in a row, but then only a couple of times since that.
There are a couple of other threads on this subject here in AF. One was postulating that maybe a rogue app was doing it. The only issue with that is if you did a factory reset and then slowly started adding apps back on, that it could take months to narrow it down due to how randomly it happens. I was going to swap my phone out but have decided to wait for the ICS update. The reason being maybe the OS on some phones had some garbage/fragmented data in it, and maybe a fresh install will solve the issue. Mostly I'm worried about going to a replacment phone, which may not have the same issue, but could have different issue(s) that are worse than this one. At least with this I know what I've got, which so far this is the only issue.
The only other thing I can think it could possibly be is leaving the phone on for long periods. I never used to leave my phone on for long periods without cycling power (by long periods I mean days to weeks) before the Rezound. Usually I leave the phone on constantly and throw it on the charger when it gets low. On my previous phones the longest I left them on was maybe 2 days before cycling power or shutting them off to charge. I'm wondering if maybe that is what could be causing the issue, similar to when you leave your computer on for to long and after awhile programs stop running correctly or start running sluggishly due to the system resources running low. I started cycling power on the phone every few days about a week ago and so far have not seen it happen again, but like I said earlier since the issue is so random and sometimes doesn't happen for a few weeks, it's hard to say that's what it is.
Sorry this got so long, but hoping maybe this will cause a Doh! moment in somone and we can find the cause for this. I'll let you know if after a month if cycling every few days seems to solve the issue or not.