In Rome (FCO), they certainly did not. I just showed the border officer my visa page and no questions asked, he stamped it and I was on my way to baggage claim. In Gare d'Nord, they looked at my visa page briefly and placed the relatively unreadable ink on the adjacent page. Immediately after the schengen border officer though, you're right, it was the UK border officer's turn.
I'm planning to go to Germany later this month. Luckily enough the visa I have is still valid. Will I have problems when I enter through them?
I am slightly less worried about the Italian case as the hotel staff took a copy of my passport and by law was required to register us.