I don't think that there would be too much wobble, remember, those wheels are huge diameters. If he is using a normal road wheel size then they are just under 28inch wheels (not includeing the tire) so that means there is a LOT of rotational inertia. If you get a bike wheel and spin it in your hands holding on to the axle then try and rotate it, its very hard (pretty much the reason why you can ride a bike is because of this, and why you can carve on a motorcycle or a road bike). The faster you spin it, the harder it is to spin. So basicly the faster he goes, the more stability he has in a straight line.
As for the movie, I think the one that i posted about a month was even more crazy where they were gravity powered and on dirt going about 100mph