I purchased a set of single coils and the middle pickup appears to have a defect. It looks as if one of the winds got caught on top of the flatwork during the winding process. This has left a realtively large single loop of slack that was bunched up under the pickup cover.

The wire is not broken. Should twist the loop tight back to the rest of the coil and solder it or what?

Best thing to do is send it back in my opinion and get a replacement you shouldn't have to fix a pickup you just bought
I agree with edwardd. However if you want to learn about making pickups the seymour duncan forum is full of very bright people. This forum I find is great for general questions, second opinions and so forth honestly.