Following 24 hour drying, sanding with 120 grit using handheld belt sander on very old pine floor, I vacuumed then damp mopped. Now I have spots of gummy poly throughout the floor. How do I proceed to fix this and move on to the second coat?
Has the polyurethane in areas other than the gummy spots dried alright? If so, then maybe these spots are the result of not stirring the polyurethane enough prior to application. Sometimes the the product settles in it's container so a couple of slow and steady stirs is needed. Second possible cause could be application method. How was the polyurethane applied? Assuming your able to access all spots and that all areas around the spots did dry properly, I would take a rag dampened with some mineral spirits to those spots. Try taking them down to a level that matches the surrounding areas.
120 grit is rather coarse for between coats of urethane. I usually use steel wool, though I realize that's not practical here. Also, a belt sander is not the right tool either. It's far too aggressive.
I'd give the floor additional time to harden, then go over it with a random-orbit sander and 220 grit. Once it's fairly smooth, wipe up the dust with a damp cloth and let dry. An additional coat or two should make for a nice finished surface. You shouldn't have to sand between these subsequent coats.
I had a similar issue when trying to take off a a layer myself, I did it with 180 grit, I'd recommend going over the floor again with a 220 grit again, once gritted, rather then mop straight away, use an industrial hover to get rid of any clumps, when you're happy mop down the floor.
My other half is OCD and was not happy -entirely- with the finish, So I went a bit hardcore and used a shaving hook to shave off any nuance lumps, hoovered and moped again.
Hope this helps