Before we all freak too much about the move over to Linux, I think it's important to note that the effect of many users is likely to be relatively minimal.
In general the term "Operating System" is a bit fuzzy these days, as the phrase is sometimes used to describe only low-level hardware and resource management software, but other times also incorporates a windowing system, application services, and a graphical user interface.
On handhelds, PalmOS and Windows Mobile includes both low-level and high-level aspects. When someone writes a PalmOS or Windows Mobile application, that app uses the graphical user interface and application routines of that OS, and thus gives not only portability between all devices running the OS but a consistent interface for end users.
Symbian, on the other hand, is lower level animal. It handles the memory, timing, and hardware management for a phone, but every phone manufacturer writes its own custom code layer on top of Symbian. Applications are coded to the phone manufacturer's layer. That's why it doesn't mean much to say one is "writing apps for Symbian OS" because the apps have to be written for each phone's custom layer, which can be widely different from manufacturer to manufacturer.
When PalmSource announced its move over to Linux, it's important to note that they're primarily talking about moving the underlying management layer (from an assumably custom system) over to Linux in order to provide better stability from buggy apps and make it easier for phone manufacturers to write drivers and adapt their hardware to PalmOS. For the most part, the layer that applications use or that customers see should not change significantly.
It's a bit like the move from Mac OS9 to OSX, but better. When Apple replaced their OS9 aged technology with a slick Mach kernel, they fixed all the memory management and stability issues while providing a somewhat-kludgy emulation system for older software. PalmOS-Linux should do something similar, but they don't need to kludge an emulation system because PalmOS apps today are already running emulated on all current devices.
A few years ago, when Palm made the move from Dragonball processors to ARM-based ones, they ported the operating system to ARM, but devised an emulation system (PACE) that ran Dragonball (68k) code seamlessly on the new devices. They (Tim?) did such a good job, that nobody notices today. Virtually all software on current devices (with the exception of HotSync and Blazer) run under PACE emulation.
If PalmSource does a decent job with PalmOS-Linux, then nobody will notice either. The only scary thing was with PalmOS-Cobalt, when they made a big push to get developers to write new applications (so called "Protein" apps) directly to the new OS instead of going through emulation, something with high costs, minimal benefits, and something almost nobody asked for. Hardware manufacturers didn't buy it, nor did most developers, which is why Garnet is still King.
Hopefully, this time they learned their lesson and will make sure all apps will continue to run, compile, and be fully expandable in the future strictly from within the emulation layer. If so, they'll get better stability and flexibility, yet I think they'll keep their existing fans, developers and customers too.