A slight inconsistency with Voyager logic is that the Doctor's mobile emitter seems to disappear when the Doctor is deactivated. That seems to suggest the emitter is holographic itself. But what emits the emitter?
With a title like that, I was half-expecting a clip show...
I was also thinking that Hologram Janeway might borrow the mobile emitter and pull a switcheroo with the Admiral, but it turns out the Doctor can just do it himself.