Any Fixes for a Dragging Caliper?

Replacing a front wheel hub, I decided to do the brakes at the same time. Usual method of using a C-clamp to compress the pistons (2 of them) to allow room for the new pads. 

After the test run, I notice the passenger side is smoking. Driver's side is not. It's not pulling to the passenger side. No vibrations.

But...that's the side I redid in a hurry. I noticed on the driver's side, one pin had a thin, rubber sleeve on the tip of the caliper pin. That rubber sleeve was sitting on the ground on the passenger side.  It started to rain (of course) so I quickly popped the caliper back off, found the pin, and replaced the sleeve.

Lests assume I didn't screw up the caliper pins. Let's assume the caliper is dragging. Is there any remedy I can try short of replacing it?

Did the caliper compress easily? If not what you want to do is open the bleeder, then try to compress it. If opening makes it become easy to compress that means the rubber hose has a blockage. If it is still difficult to compress that means a caliper problem. 

But if it wasn't dragging before the repair and now it drags hard enough to actually smoke then I think you put something together wrong.

I've had way more swollen shut brake hoses cause dragging brakes than I ever have sticky calipers. 

Could the smoking be the slide pin grease burning off?  With the wheel in the air, how hard was it to rotate the tire?  I think it would be unusual for a caliper to be so tightly sized that it would smoke but you wouldn't get any sort of odd handling from it.  Was the whole wheel hot?

I'm having a hard time visualizing the rubber sleeve that you're talking about.  I'm assuming that it's some sort of grease seal?

The above advice is what I'd do, too.  If it compressess okay when it's off the bracket but before opening the bleeder screw, then I'd make sure that everything was greased up and that the various bits of brake hardware and springs are installed correctly.

Why are my calipers in 4 peices?

Phenolic pistons?  I have never owned a car with them, but I have heard that those are fragile and need to be compressed across the entire face of the piston, rather than just using a corner like you can with a metal one.

Not sure why that would cause smoking though.

I've done plenty of quick and dirty brake jobs with the rubber/plastic sleeve was left off then slides and didn't cause a problem.

Most commonly drag on only one caliper was caused by hoses like Cousin Eddie said. I have had a bad caliper or slide cause it. Slides are easy to check, do they move ok? Then they are good. Caliper is a little trickier but hoses are cheap

I'd stick a hose on it.

Turns out slamming it back together in a hurry was dumb. And expensive. I saw the clip was janky.

New caliper, and all is right with the world