It would have been useful if they had filmed two versions with different audiences but the same arguments put by the same presenters, and compared the results.
I'd be surprised if both groups chose the same artefacts to destroy (particularly if they were matched demographically), which would prove the point that these things are arbitrary.
FWIW, (and bearing in mind that I saw about 10 minutes of the programme, which didn't include the photo of the child) I would probably be inclined to destroy that, as there are issues of consent attached to photos, which a 4 year old cannot give. I'd probably vote to lock away the Hitler, so that it couldn't become some sort of icon for neo-Nazis. Rolf Harris' art was pretty disposable anyway, so I would let it stand, and hope that nobody who couldn't afford to lose money hadn't spent a lot on it. I would move the Gill statue to a museum and stipulate that it had to be displayed next to an explanation of his behaviour, so the work would survive but his reputation would not, and I can't help feeling that Picasso's work rises above anything he did (although I don't really know the extent of his transgressions).
My guess is that most of us on this thread would vote differently in at least one case though, so it's probably better to leave things alone and let time be the judge. It pretty much always is where matters of Art are concerned anyway.