When pilots complain about rudder trim or aileron trim needed to keep the a/c level (more than 1 unit), first check the cable tension of the aileron wing cables ABSA and ABSB in LH and RH wing. Very often the cable tension of these cables is far too low, causing a sloppy aileron (control) due to the low cable tensions. The cable tensions can drop as far as 50% from the required level ! Especially with flaps not up this can cause trim problems. Make sure you adjust the aileron positions and cable tensions exactly iaw amm:
737 Next Gen: task 27-11-00-820-801
737 classic: task 27-11-00-825-001
Also check the neutral position of the rudder compared with the rudder trim-indication in the cockpit. Often these positions are not exactly matched, causing a false rudder trim complaint. ( Of course the rudder system must be rigged exactly to zero iaw the amm. ) But it happens that the trim indicator has some deviations compared with the real rudder trim position. A quick and simple procedure is to adjust the zero-indication of the trim indicator on the bottom of the indicator-module.
After checking and adjusting the aileron cable tensions and the rudder trim indication, the complaints are often solved.