my ford does but i have never seen this as a fault on this or any Fiat.
Consider yourself lucky - my Mk1 Punto, Mk2 Punto and Stilo, plus at least another one Mk2 Punto i've driven have all had the dodgy indicator stalk.
mk1 punto was the red lever under the dashboard drivers side...kinda directly under the steering column.
Yup, you had to clasp it almost like you were sticking two fingers up at someone and pull it towards you. It was in a similar position to very old Fords - our X reg Escort had an orange lever in a similar place.
All the Fiats i've had have had driver side bonnet releases. My 02 plate Clio's was on the passenger side though (and the wipers went the wrong way!)