Very lately and very randomly I have felt some dragging. I thought it was a low or flat tire the first time it happened. Checked at home and tires were fine. Did great a couple of days until it happened again. This time I noticed it in stop and go traffic on our interstate. After breaking a few times, it returned and seemed to lope worse. Again felt like a flat tire. Makes the steering wheel wobble when its bad. Then it would go away and roll fine. I noticed this weekend the fuel mileage was going down a couple of tenths. This afternoon it happened again and stayed bad long enough that when I stopped on the off ramp, a good cloud of smoke rolled out from the drivers front side.

What could be causing a random hang up on this brake?

 

Sounds like a rubber line is collapsing inside. When you put the brakes on, it pushes the broken piece forward
when you release the pedal, the broken piece stays put, keeping pressure on the caliper.

 

It would do that randomly?

 

Yup . Check the slides and pins also.
If hot enough to smoke, a full rebuild is in order.

 

Try bleeding the lines starting with the furthest caliper from the reservoir. Give that sticking caliper a few taps with a shop hammer too.

 

Had the same issue, had to replace front driver’s side brake caliper, not happy. The caliper was only two years old!