At the start of the flight ID operation in germany we had a few problems like that in our 733s (single FMC, re-fitted transponder). Displayed flight ID for our ATCO colleagues was often a wrong ID or the one from the previous sector, however that happened only in the bremen FIR. Apparently it was a software problem in the radar tracker software in that FIR with those special transponders, it was solved with a software update on the ATC side of things.
Currently i am not aware of any problems like that on our dual FMC 737NGs (nor on the airbus fleet), only that sometimes someone forgets to put in the right ID. The latter grows into an important matter as germany moves into flight ID only for IFR flights, an operation which is currently tested on selected routes and where you only sqawk 1000 and the ATC system tracks the flight ID and not the squawk.