Those dents looks small but deep, as if it hit something when dropped. The metal has been stretched into the dent and needs to be compressed to smooth the surface and match the etrernal curves. A burnisher or wooden spoon if possible) on the inside will remove the shallow dents (as seen on the right side in both pictures, I believe).
A snarling iron is a long (12"+), tapered (1" at base, 1/2" at end) forming stake with an upward turn near the end and a ball terminal. The base is secured in a stump and the object is placed over the end. Holding the object the base is struck with a hammer causing the ball end to vibrate against the inside of the piece while a dolly is held against the outside. The inside of the dent is worked this way until the metal has been gently compressed and then without the dolly to bring to outer shape smooth with the undamaged surface.
Here is a link to a picture of one: http://www.google.com/imgres?imgurl=htt ... A&dur=3944