Those marks will never come out despite what others have told you Imperfections such as brush marks and globs can be sanded smooth then put down another coat of poly. The next coat should be with an oil based poly. I am guessing he used water based poly over oil base which is why it is flaking and peeling because it didn't make a uniform coat and some spots may not have adhered. Tell him to make sure he brushes with the grain in the future when he does wood finishing and to not over stroke the finish or apply a lot of pressure, then the strokes wont be as noticeable. You cant just slap it on there in any which direction and it turn out nice. Also use a fine hair brush, he probably just used whatever brush he had. Did not help he dripped in certain areas either. Most pros use a lambs wool applicator or a hardwood floor polyurethane roller instead of a brush for floors. Nothing wrong with using a brush on other wood projects though. More info on technique http://www.gandswoodfloors.com/polyurethane-floor-finish.html

Spot repair using polyurethane is problematic since the finish does not 'feather' well. That means the finish does not blend with existing surfaces in a repair area easily. So, what I have successfully done on several occasions is to start with 100 grit paper(I favor a random orbit sander) and get the big problem areas smooth and chip/flake free. Don't worry about defined edges, just get the problem spots.The random orbit sander is much faster than a 1/4 sheet sander. Then switch to 150 grit paper and get the sanded surface smooth. You want to use the same type poly as when you refinished. Use a rag dampened with paint thinner(if you are using oil based poly finish) or water(for water based poly) and remove all the dust/etc. Apply the poly on the sanded area, using only enough to cover the sanded area. For that small area, a paint roller with a thin nap(thicker naps will cause bubbles)---1/4" nap is fine. Now for the blending/feathering. I use a cotton Tshirt as the feathering tool. I use a piece about 12" square or 6" wide and 12" long. I fold it until it makes a ball with a smooth surface. I dip it in poly and begin wiping the edge of the fresh poly in a circular motion, moving outward until the pad is dry. Then move back into the fresh poly and keep up the blending until the entire perimeter is done. You do not need a lot of pressure. And you will find the best method of wiping as you proceed. Since you will need three coats of poly to complete the repair, you will be able to lightly hand sand the perimeter before another coat.

wannabath - you are absolutely correct. You get what you pay for. But I had floors refinished in my old home many years back. Also oil finish and no issues like this. My project is a kitchen renovation being overseen by a GC. (My cabinets and countertops were ordered and installed through a cabinet maker.) Everything else organized through the GC. It is the flooring guy he uses on all his jobs. I installed new wood and had it sanded and finished, so I don't have a px just for refinishing....I'm not saying all cleanup would be as meticulous as Lyndee Lee...and I am not expecting perfection...but he was definitely sloppy, He created all the dust, he should have done a better job cleaning it. He was also a little careless with my cabinets. Some small bangs/chips, some polyurethane splashed up on the bottom of my cabinets. Why wouldn't he cover the bottoms with some painter's tape? He only covered the bottom openings for dust. No protection from the liquids...and I asked him about it. He said not to worry, only the very bottom of the cabinet base will get some stain (and thankfully no toe kicks are installed yet). Well that was clearly not the case. **I am glad to hear you think the bubbles and nibs will flatten out over time. That is what I am most concerned about.** The flooring guy is very nice, but I realized I am not happy with the caliber of his work. No sense to make him come back and redo. it probably wouldn't be any better,...and then I run the risk of more potential damage to my new cabinets. I would rather live with it as is...and for some reason if it doesn't improve down the line, I will do my own research and select my own flooring person.

You will need to sand it down to bare wood. Use a steel brush to hand wire brush the floor before aplying any finish.