Is it possible to build a linear telescope? I.e. with a linear lens/mirror, focusing into a line instead of an area, like a scanner or photocopier does. And would it be of much benefit in terms of aperture? (I'm thinking that a 12" linear mirror focusing into a line should produce more light than a 12" circular mirror, but maybe I'm wrong there).

It'd be useless for visual work, but could be a lot of fun for imaging. You'd use an equatorial mount, align it, then position the scope 'ahead' of the area you wish to image, and start recording. You don't need tracking or motors at all, because the area you're imaging passes through the slice you're aimed at as the earth rotates - you just wait awhile.

I've already written some software capable of imaging from a setup like this (it's called slitscanning in photography). I suspect the hardware setup wouldn't be too hard (this type of CCD array is easily found in the average scanner.. which also happens to have drivers (often open source) available. You'd just need to be able to read from the CCD array, after that it's pretty easy to do the processing. A large parabolic linear mirror seems easier to make - I'm thinking of the curved mirrors in the traditional 'hall of mirrors' here, but perhaps I'm wrong as I know near zero about mirror making. But if large, cheap mirrors are possible, this could be a fun project.