Omnidirectional means "in every direction", so an Omni mic will pick up sound from all directions, not only your desired source...
Based in my experience some of the pros and cons are:
Pros: (If you want it) it picks the natural reverb from the room in wich you are recording, that can make it sound beautiful.
It is also useful for avoiding proximiti effect.
cons: a lot of leakage when tracking more than one source simultaneously but with different mics. (it has no rejection in any angle)
it picks the natural reverb from the room in wich you are recording (if you DON'T want that it's a big problem)
and many others I can't remember
Peace.
PC