How can I pick up the motorcycle when it's fallen down?

When the Jawa motorbike is on its side go ahead and mount the vehicle as the driver. You'll now be on the motorcycle, which is still on its side. Then push the side movement key (right or left - whichever is applicable) and voila! The motorcycle turns upright with you on it.

(With thanks to OFP player Chris G. and to squadmate Uzi for the heads up).