Rob,
The lose wire is for the "coil lock out" coil. It should not be floating around as it will short and cause all sorts of weird issues. For now - either solder it back on to the coil (test the coil is not a dead short), or use some electrical tape to cover the wire.
Second issue is the burnt out coil. That would be for the "10,000" score reel - or the score reel to the LHS ? That is most likely burnt out because there was a playfield switch stuck permanently "on", or the 10,000 unit did not dis engage. I do have a schematic and access to my dis assembled Pro Football machine. I guess we need a coil first up ?
I'll have a look for my schematics...
BTW - the score reel is not missing the board - not all the score assemblies have the board !