Hi Platonides,
this is a great idea, but requires much work; we'd probably need to
make a crowd-sourcing effort to get at least a small list of such
objects. As far as I remember, Emijrp wrote a great essay on the
subject last year, so we'll only need to add the list.
I see that the Global Heritage Fund has identified such a list for
Syria (see
<http://ghn.globalheritagefund.com/uploads/documents/document_2107.pdf>),
so maybe going in the direction of countries currently engaged in a
military conflict (Wikipedia provides us with a list at
<http://en.wikipedia.org/wiki/List_of_ongoing_military_conflicts>)
might be a choice.
On the other hand, a Google search for "damaged cultural heritage" (in
Polish) directed me to an article on the 2012 Northern Italy
earthquakes (at
<http://en.wikipedia.org/wiki/2012_Northern_Italy_earthquakes>), so
maybe this direction good help us list some other damaged monuments,
too.
Just my three grosze.
Thanks,
Tomasz