Both of those are common problems. I quit trying to keep my neutral light working years ago. The 4 to 5 false neutral I think is in the design; you just have to make sure to shift very positively, especially on that one. Last year I converted to GP-pattern shifting, and that helped with it as well.
1993 Ducati M900 Monster "Patina" (242,000 miles, so far) -- 1995 Ducati M900 (wife's bike) -- 1972 Honda CB450 (daughter's bike) -- 1979 Vespa P200 (daughter's scoot) -- 1967 Alfa Romeo GT Jr. (1300cc) -- 1964 Vespa GS160 (160cc 2-stroke) -- 1962 Maicoletta scooter (275cc 2-stroke) -- 1960 Heinkel Tourist 103A1 scooter "Elroy" (175cc 4-stroke)