The paradox related to omnipotence is well known - in one of the many possible forms it asks whether an omnipotent being can create a stone that it cannot lift.
While there are many similar paradoxes based on self-reference (like whether the adjective "not-applicable-to-itself" applies to itself), I do not know any other paradoxes related to the aspect of omnipotence expressed by "omni". For example, I do not know whether omniscience or omnipresence leads to any paradoxes.
Does anybody here know any such paradoxes?