2005 Audi A3 passenger side window keeps going up and down by itself

You have got a ghost !!! Seriously , strange fault . As it is only affecting one window , the only thing I can suggest is to check switch / wiring for that side . You could disconnect switch and see if it is ok then . Either that or check wiring at window motor .Really a case of stripping down and tracing through circuit for fault .Dont know if a faulty relay would cause this intermittent fault . I am not an auto electrician , so this is all I can suggest to help .

One of the common faults in door electrics is where the wiring passes from vehicle to door at this point wires have a habit of breaking and end up moving about and touching intermitantly.
Failing that i'm pretty sure that the windows can be accessed by using a code reader which will no dought have a fault logged

if you nhave a factory fitted alarm / immob it has a fault which can be sorted by someone with a vag com 1 diag machine