A few weeks ago my wife's 2006 a3 had its camshaft replaced. When I took her car for a ride I noticed that there was a loud noise coming from the engine bay. I looked under the hood and notice that one part on the left side of the engine, near the belts, looked as if it was not reinstalled correctly. I have circled the part in red. When the car is running, that part is vibrating a lot..see video. Is that normal? Thanks!

http://s234.photobucket.com/user/aberle99/media/20160103_134731_zpsagwddm9b.mp4.html

 

As long as it does not come out it should be OK. Looked at mine and it does not move, at least the pin itself, unless you are referring to larger piece and not the pin. The whole thing does move, does look like it vibrates as it is riding on the belt. Some type of idler pulley? Appears to just be a pin, not a threaded piece. I think it is just there to limit rotation within the area between the raised ridges above & below it.

 

Thanks for looking... I suppose my wife will see what they find out at service tomorrow...

 

I'm pretty sure that is your pulley tensioner. I don't recall that rusty looking pin sticking out the back on mine - that's the only thing appearing to be odd on your setup. However it does move while the engine is on.