I've owned a Ducati Monster 600, a Supersport 750, and a Supersport 900ie. All apparently from the era of "dodgy" electrics, ha!
The monster had an electrical fault, at 10 years old and 42k miles it needed the rear indicator lights replacing because the connectors had corroded. Cost me £16 from the Ducati dealer for the parts and took me 10 minutes to fit them. It was my first non-125 and I sold it after putting 28k miles on it commuting in all weather and at all times of the year. I dropped it countless times through my own stupidity and it held up very well, never needing more than a lever or a front indicator. Only visible damage was scratches on the exhaust and the bar ends. Otherwise it had nothing wrong with it the whole time I owned it and all I spent was on normal servicing.
The 750SS had 1 electrical fault, someone in the bikes past had put the airbox back in badly and trapped a wire from the regulator/rectifier against the frame where eventually it wore through and the wire needed replacing, a free fix. I owned this bike from 1000 miles and put another 30k on it commuting in all weather at all times of the year before I sold it. Again only tyres and servicing required.
The 900SSie is currently my race bike so I can't really comment on that. No problems with it so far but it does get fussed over and none of the road gear is left on it to go wrong. It had 19K miles on the clock when I ripped the speedo off it.
Hope you appreciate some informed and first hand experience of Ducati's. In case you think I'm some sort of Ducati fanboy I've also owned: Kawasaki AR125, Honda NSF125, Kawasaki ZXR750, Aprilia RSVR Mille, Suzuki GS500 and my current Suzuki 1250 Bandit.