Multiplayer. LAN server at work which I also access from home along with another friend who uses Macs.
When I arrive at a certain co-ordinate my FPS drops from 60-70 down to a reported 5-10 however functionally it is much less. The screen locks for a second every other second. Turns become 90 degree jumps. All animations ~(water, torches) lock for a second. As I struggle away my character walks in thick treacle (even when the lock-up is not locked up) which slowly speeds up as I get further away. I never noticed this issue in any previous versions although I may not have been to this location for a long while.
Problem occurs along the same X axis at any Y axis and over a long-ish Z axis e.g. I have seen it happen at 310,54,27 and also 311,65,-22. Not encountered it anywhere else yet.
Issue is easy to re-create simply by teleporting to 310,54,27 on my World.
(Access available if necessary to trusted developers)
Smooth lighting is off. View distance has no effect.
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Please force a crash by pressing F3 + C for 10 seconds while ingame and attach the crash report here.
As requested...

When you say LAN server do you mean to say you are using the Open to LAN option, or that the server is hosted locally?
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.)
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.

Is this occurring in areas with a high entity count? (eg mobs, item frames...)
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.
Caves.
I noticed on the crash report that there are a lot of paintings in the area. Could that have something to do with the situation? (Yes, paintings count as entities too.)
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 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.
Both locations with paintings operate normally.
Is this still a concern in the current Minecraft version? If so, please update the affected versions in order to best aid Mojang ensuring bugs are still valid in the latest releases/pre-releases.
I've added the latest version although the problem is now much less severe.

Resolved as duplicate of MC-12799