For an AC extension cord, the net induction from a coil of macroscopic size should be practically zero. The current that flows one direction (and sets up a magnetic field) is cancelled by the return current flowing in the other direction down the neutral conductor. If it isn't, you have significant ground leakage or other major electrical problems.
Heating is the main concern, and that has more to do with wire being confined in a small areal than with it being in a coil per se. A coil is, of course, one efficient way to get a lot of wire in a small space. (Heating concerns also have to do with the current that is flowing with respect to the wire size, and to other environmental conditions. In particular, a black wire in the sun can get pretty warm even when disconnected, so it's probably more important to be careful under those conditions than with a wire on a reel in a storage compartment.)
