I consistently get this issue when entering a minecart too. My character sits down but is too high so when I try to click the 'start' button (even one that's at head height, a block above the track) I actually get out of the minecart. However if I wait ~2 seconds then my character sinks down into the cart and allows me to click 'start' just as it worked in 1.4.7 and previously.
Are you sure you're not being killed by an invisible player who is then stealing your items? What's your death message?
Both locations with paintings operate normally.
I think it's unlikely though - I see there are many more paintings listed in the crash dump - the only other place I have paintings is at my mansion about 3-400 blocks away and I experience no problems there.
I do have an art gallery a couple of hundred blocks away where I display one of each of the 26 ( ? ) paintings. I'll go directly there shortly to see if that area lags too.
I'm at the end of a short tunnel near the surface. No mobs or anything that I can see although the crash dump does seem to list rather a lot.
I have closed the server, copied the World locally and the issue still exists on Single Player (on my PC at least). I can upload it somewhere if you wish but it's 500MB before any compression.
It is a dedicated machine on our work LAN running the minecraft_server.exe. (The machine has latest Java installed and we've already tried rebooting it.)
We both play by connecting to it via the LAN during lunch and also over the Internet from our homes (port forwarded on the firewall.)
As requested...
I've added the latest version although the problem is now much less severe.