The scriptwriters established a rule: you can only use the transporter at warp if the thing you're transporting to is going the same speed. (They thought that transporting at warp seemed a little too miraculous, but they didn't want to write themselves into a corner.) As it turns out, later on they found themselves writing an episode where they needed to transport at warp, and there's a throwaway line about "synchronizing speeds".

(I forget where I read all this ... maybe the Star Trek Technical Manual, maybe The Physics of Star Trek.)

Oh, too cool, that works perfectly for my story. Thanks.

'twas in the Next Generation episode 'The Best of Both Worlds', where O'Brien makes a throwaway comment about synchronising warp speed for transport over to the Borg cube they're chasing. After that it was pretty much set in stone that you can only transport between ships at warp if they were going at exactly the same speed. Presumably the transition through the subspace fields generated by their warp drives would scramble the transport beam if you're going at a different speed.

And that would be very, very messy. Ick.

Something else though - if someone's beaming onto your ship after matching warp velocity, and you don't like them, just accelerate a little halfway through the process. You've got a second or two during the transmission phase in which to make them leave their legs behind... I think I'm in an evil mood today.

Yeah, they did this in Voyager as well. I think it was the season 4 finale... let me check... yes: http://www.st-hypertext.com/voy-4/hope.html

They were in a quantum slipstream (imagine warp speed, but really, really fast warp speed :-) and needed to beam Janeway and 7of9 off an alien vessel. Even then, they needed to match velocities in order to beam.