Genius! Thank you both for your excellent and speedy solution! This animation is going to look great :D

Ack - I've worked out what the problem was, and it's not specific to single sided objects, it's true of all the square props. I had a square with a movie on it and another sqaure ever so slightly behind it which was slightly bigger (it was acting as a border or frame to the movie). When 3d motion blur was used, the movie was being blended into the frame behind. Not good. Moving the movie away from the frame fixes the problem. I dont know if this could relate to some other setting (like displacement... I'm not too clever with those settings yet) but it's pinpointed the problem at least.

Late reply here :) You can put the avi as a background and you will see it in the work view. Use that to animate your figure to match. As for issues with avis on props... well, they work ok for me.