That yellow side light probably only has one wire for power and uses the frame for ground. The wire hanging loose is probably not used, at least for that light.
Even if the "repair place" were next door, I would not take it back to them. That looks like one heck of a mess. It would bug me so much I would just go buy a new trailer harness assembly, rip out that mess that is there, and rewire the whole trailer. In the future when you have problems with one of the lights (and at some point in time you will if you keep it long enough) and have to troubleshoot it, you will appreciate having it wired properly and the color code correct.