For anyone curious, I figured out what was going on. The mosaic when brought into a WGS 1984 map lined up perfectly. When I brought it into a NAD 1983 map and let it re-project on the fly (which is what I had been doing) it was off by 3-5 feet. When I brought it into a NAD 1983 map and instead set the transformation using WGS_1984_(ITRF00)_To_NAD_1983 it came in fine.