I had my reclaimed heartland pine floors refinished by a professional company who specializes in such floors. Stripped down to wood, no stain, three coats of oil based polyurethane with sanding in between. The floor has these white marks in numerous areas that look like tire treads or sneaker marks. The owner says this is common and can be easily fixed but I am nervous. Any ideas on what caused it and how it can/should be fixed. I am concerned I have a botched job (for which I paid a small fortune) and he is not going to fix it adequately.

There are different reasons for uneven color of a floor after refinishing. Over a rather short period of time the wood will amber and the oil based poly-urethane will yellow which will help the color even out. Some brands of poly-urethane "amber" more than others.

Ginger . I'm late to this party but I would recommend posting some pictures . Sounds like sneaker marks from walking through the finish . And if that is the case , it isn't common because it shouldn't happen .
The only way to fix this is to abrade the finish and re coat .This assumes that the sneaker marks aren't buried under a layer of finish above them .
Either way , there shouldn't be anything white in your finish when oil based urethane is on them .