am I opening myself up to future problems if I spread the POD through the module and document each method next to that method's code?

No, you are not. The placement of the POD is mostly a micro-optimisation and can therefore be ignored in most cases. The all-the-POD-at-the-end rule of thumb is only really relevant when preceded by an __END__ so that the interpreter stops processing the file at that point. I guess that's the very strictly correct way to do things but the benefits for a module without MegaBytes of POD are so slight that it's pretty much irrelevant.

Unless/until you are writing a module which is used almost everywhere, the POD placement really isn't worth worrying about IMHO.