I haven't remembered what the mop was for yet. I haven't remembered anything beyond that night. It couldn't have been anything TOO dire because he almost forgot it, so probably something more...on the way, quick fixing type thing.
But yeah, he went back and forth that many times. I couldn't tell you what it runs on. You'd think it'd take a lot of energy...
Though the bigger thing might be control. The Vortex Manipulator was pretty smaller, but the Doctor did say it was rougher form of time travel. While the TARDIS has a big console. So it might be better because there's more...things to make it go where you want to.