I had aerobars put on my '04 Specialized Allez Elite yesterday and took the first ride with them on the bike this morning. I only used them in spurts. I was pretty unstable at first but then grew more stable later in the ride.
As far as I can tell, riding in the aero position makes a bid difference. I was surprised a number of times when I would look down at my computer and see what speed I was cruising at. It was generally about 2mph faster than what I would usually do. It also make a big difference going down hills. I have read that aerobars generally make about a 1mph average difference. I believe it.
Question - is the aero position generally used on the flats and down hills but not up hills?
I would not use the bars on anything more than a slight uphill. Their advantage is not noticeable under about 18-20 mph (unless you're in a headwind). For the hills, it's more beneficial to be able to breathe as easily as possible and apply steady power to the pedals, that's why all the pro's will use the tops of a drop bar on a big hill. Also, try to get up the hill as fast as you can and allow yourself to lose a little speed at the top for a short time while you recover. You have to balance that effort vs recovery, but the uphill section wrecks your average speed so it's really best to get up the hill as fast as you can.