Yeah, the option to not have it running with the persistence is in settings. I've found you almost never experience a problem like that, but very rarely if you are loading the CPU (this happened to me once while using several tabs in dolphin browser) the OS can stop the myLock process. Now normally when that happens, it restarts it within a short time. But if you happen to lock the phone before that restart, you'll get a lockscreen next time you go to unlock, and that might break your functionality in the Lite mode or other past release versions.
Could you guys describe the handcent issue? Was it just that you lose functionality? My new modes seem to allow the popup. These modes work by displaying a custom screen anytime the phone sleeps, overriding the lockscreen. If the phone sleeps again the popup is gone, does handcent normally keep it there on screen till you've done something with it?
I noticed handcent also provides the option to display popup only after unlocking, I bet that would stop it from conflicting and actually cause it to display properly after myLock does your unlock for you.