Ok thanks for all the replies, I've just tried the incredible ruler trick and that causes the same problems. It seems to only happen where I have the logic lines crossing over, I don't know if that might have some significance...I can't really see how it could though since they are simple logic signals, not high frequency or anything.
Anyway I'm going to rewire it all now, and carefully go over the connections to the PIC again to make sure I haven't left anything floating. Will report back ASAP.
EDIT: Oh I thought I should add, I'm not using a crystal I'm using the internal oscillator instead.
The displays are driven by display driver ICs, yes. The problem seems to be in the lines from the PIC to these drivers. The interference only seems to occur near these wires. I haven't tried swapping them, that's a good idea, although there are three and they all have the same problem.
The circuit's in a breadboard at the moment, will that affect the effectiveness of the ground connections? I was toying with the idea of wiring ground on my circuit to actual ground, like my computer case to see if that made a difference.
I have checked all the connections and they seem to be correct, but like I said I'm going to rewire that part of the circuit and see if it helps.
And no, I don't have a scope, just a very cheap and crappy multimeter unfortunately. I hope to get all of that good stuff one day, maybe have a workshop setup like Dave has.