I'm not sure what services PalmOS provided to the apps, but to my limited knowledge the apps themselves were non-multitasking, and had a standardized database per each app instead of the filesystem (i.e. something like proto-IndexedDB, but more oriented to documents or blobs). So it's kinda difficult to imagine them having the problems of quasi-multitasking and more complex MacOS. But perhaps things became involved by PalmOS 5.
Though the event handling part sounds like DOS' raw approach, versus Win95's abstraction—and I guess could plague any kind of a system.