I'm going to assume some things here .... you're Calphalon aluminum is probably going to be anodized and a dark grey color ... and the film you are talking about is on the outside bottom of the pan, not the inside bottom of the pan.
If the film is a white powder looking coating, it's probably a water mineral thing - but since some pots/pans have a "film" and some don't, and the vinegar/water didn't remove it .... I'm guessing that is not the problem.
I'm guessing you are experiencing the same problem I had .... grease. If you cook on one burner and the ajacent burner is not covered, a film of grease can get on the burner and on the area under the burner. Then, when you use that burner ... the grease can heat up enough to smoke, and that is going to form a grease film on the bottom of your pan. Over time, if not removed, this will form a layer similar to what you get when you season a cast-iron skillet (heat fused grease).
For this - you need a spray bottle "Murphy Oil Soap", a can of Bar-Keeper's Friend or Bon-Ami, your regular liquid dishwashing soap, and a green scrubbie like Scotch-Brite or some other brand.
(1) Run some warm (not hot) water on the borrom of the pan to get it just warm and wipe dry.
(2) Spray with Murphy and let sit a few (2-3) minutes
(3) Gently scrub with scrubbie and rinse with warm water
(4) Repeat steps 2-3 a couple of times until the film is gone
(5) Wash with scrubbie and Bar-Keeper's Friend
(6) Wash with liquid dishwashing soap
(7) Rinse and dry
The Murphy oil soap helps melt the grease and the scrubbie is just abrasive enough to help remove it without scratching your pan - unless you really go crazy applying pressure. The Bar-Keeper's Friend is a very gentile abrasive that cuts the oil from the oil soap - but it can leave a powder residue. The dishwashing soap get's rid of the residue from the Bar-Keeper's Friend.
"It ain't what you don't know that gets you in trouble. It's what you know for sure that just ain't so." - Mark Twain