Your LT does not have any electronic controls or sensors related to the transmission; it is a very conventional mechanical box. The Motronic controller will monitor and store failure codes related to engine sensors and to ABS only. As a matter of fact, even the engine computer cannot be "updated" over the diagnostic connector - to the best of my knowledge - map changes can be effected by replacement of EPROM.
Almost sounds like either the dealer was giving you the STORY, or you simply misunderstood what they were telling you.
Regarding shifting: you are probably aware of it by now, but if not: the LT gearbox is rather clunky. Not the best example of German engineering, IMHO.
It works best when being preloaded for shifts: i.e., put a little pressure with your foot on the shift lever in the direction of desired shift, then "blip" the clutch lever while letting the shift lever move, then release shift lever. This allows the box to smoothly fall into the desired position.
And yes, occasionally you will still find yourself with missed shifts or a false neutral. "They all do it..."
Same thing for the wrong indicator: it happened to me a few times as well (having indicator show 1st, while bike was in N, or vice versa). I usually rock the bike a bit while parking nowadays. Don't ask how I know.
All of my BMW gearboxes are reluctant to shift into 1st while standing still in neutral. The standard technique is again to preload lever towards the 1st and partially release clutch just ever so slightly, to impart motion onto gears. That will align the otherwise motionless gears and allow them to slide into 1st.
You do not encounter this issue as much when the bike is cold, because the trans oil is more viscous and drags the gears into position.
Still, these are quirks. Fine machine overall. Not sure if the same statement applies to the dealers.