I concur with the theft advice, lock it, lock it, lock it. That really is the only threat to your bike on a trunk mount. The only real thing that will hit the bike (excluding someone rear ending you) is rain, and there's not much you can do about that, because like someone said you cover the bike with a plastic and the wind will just rip at the plastic and blow it off or shred it all the while your screaming at your passenger so you can be heard over the noise!
There are some things you do need to to when under way. Once you secured the bike onto the rack and start out driving, drive about 5 miles or so get out and recheck the tightness of the security straps, then do it again at about 20 miles out, after that just check every time you stop.
Another thing you could do if your really worried is to buy some foam pipe insulation, cut to fit your forks and stays that face the body of the car, and top tube so the brackets that hold the bike won't slightly mar the paint while the car is bouncing down the road. Make sure the openings of the foam is facing to the rear so wind won't catch the opening and blow it off.