Directional Lag?

If, and pretty much only if, your chunk update rate was jumping around, it could be due to a redstone timing error in the game. This has been seen before in the game. However, your chunk update rate is stable, it's just horribly low. That pretty much sets it as on your end, as redx475 has already said.

 

As for the rendering issue, this happens when I look in a specific place, while it is rendered. This means that is is a definite... thing that is causing this for me and others.
(As far as I can tell, it has always been on or at least near a quest NPC). I believe that this problem could be fixed on both ends, by either finding and removing/editing the faulty entity/block, or by experimenting with rendering and applicable rendering settings until it is determined what algorithm is causing the lag. I will further experiment in the future when I have some free time, but perhaps someone will resolve this before then.

 

Once again: This is more than likely not caused by an entity. It's caused by there just happening to be too many things that your graphics card is trying to render. It just so happens that looking at that spot means there's some extra stuff that is eating up CPU time. It could be lots of transparent objects, it could be something to do with the lighting. That's it. End of story. We can't do anything to fix that, it's purely a quirk of how rendering 3d graphics works.

The only possible way I could see even finding out what causes it is attaching an OpenGL debugger, at which point I'd most likely find out that, hey, there just happens to be a few more transparent blocks in the frame when looking in that direction.