If I am playing Omnitron-X, and I play Slip Through Time early in the game, before I get a second power, can I use my base Timeshift power a second time? It seems from the rules that I probably can't, but it's just uncertain enough that I'd like to hear confirmation one way or the other.
Nope. Each power can only be used once per turn.
No. Each power can only be used once on your own turn, unless a card specifically says otherwise. The only card that I can think of that does this is Mr. Fixer's Overdrive card.
Just to clarify, each "instance" of a power can only be used once per turn.
Use OmnitronX for example. If he had two copies of Bio-Engineering Beam in play, he could use them both on the same turn when combined with Slip Through Time.