Outside of the crew neglecting to input the flight number in the transponder another issue is the use of alpha numberic callsigns as opposed to alpha numeric flight numbers.
There are numerous instances of this such as Ryanair 9C4D, Speedbird 9D, Midland 9EV and the like. These callsigns ( which are usually a mouthful ) are presumably deliberately made up to avoid mixups between similar sounding flights in the same airspace.
There is usually a fixed tie up between the callsign and the 'correct' flight number. From what I can see the crew often input the callsign as opposed to the flight number which would require the flight number to be replaced by the callsign in the database in order to get the routing to appear on the map or log.
With regards to bizjets, Net Jets along with a significant number of other executive operators operate both a flight number system and a fixed callsign, the latter of which ties into the aircraft registration ie NJE 6VL = CS-DFR.
In Net Jet's case the the first digit of the fixed callsign ( after Net Jet ) indicates the aircraft type - examples such as 1 or 7 for Citation 550, 2 for Falcon 2000. From what I have been able to observe the fixed callsign ( with Net Jets ) is used for a/c positioning whereas the flight number is used for revenue sectors.
Again, presumably this sytem was adopted initially for busy airspace around airports like Luton where 20 % of the aircraft would have been calling - CS-D**
A good listing for fixed callsigns for bizjets is to be found at :
http://www.antonakis.co.uk/acars.php?page=callsignsSo far though I haven't seen any Net Jets with either the fixed callsign or the flight number showing on RB.
Gerry