I have a 2012 FLSTC and it had a wobble before 1,000 miles. Turned out to be very, very loose spokes. The dealership said they got a notice from the factory to check them, but for some reason they didn't inform the owners until they brought it in.
Same here 2012 FLSTC Loose spokes. Now on my 3rd rear rim 8000 miles they promised the problem is fixed this time. Yea Right changing to mags over the winter