Sounds a bit similar to issues I had a year ago approx. Reverse only. Got it towed, mechanic started it up and drove it normally! No explanation, he talked about possible actuator etc, but I doubted it, thought more sensors, contacts, battery etc. Months later it played up in a similar yet different way, would go in first or R, nothing else. Drove in first to mechanic (close to me luckily), he topped up a tiny bit of SS fluid, off it went. He thought the amount of fluid wasn't enough to have fixed the issue so something else going on, but couldn't be sure what.
Another time he ran a SS calibration routine using the examiner, which solved an issue of some gears not being selectable. (turns out I could have done that with AlfaDiag, but didn't know it at the time, plus engine needs to be fully warm etc, so need to be careful).
Anyway, now got a different issue (see my other thread about won't start). I'm suspecting it's all related!! (hey same car as mine after all)
In the meantime, keep a spanner handly, unscrew battery terminal closest to front of car, wait 15 mins (no less), replug in see what happens. Fixes most issues I've had in the past year!!
My guess is electrical contacts/sensors/earths need a good clean and overhaul or replacing. But just a guess.
I don't trust mine either, which makes for slightly stressful motoring (esp in peak traffic which I avoid!), but she's a good girl overall, couldn't leave her. (until a younger GT or GTA comes along anyway)