Enderchest texture is buggy / Mob & player characters partwise transparent

When looking at an Enderchest or a chest next to a invisible spider, some of the chest texture is dissapering. When looking in F5 modes, it looks like your behind the chest and sign, and your skin gets all wierd and mixed up
Video: https://www.youtube.com/watch?v=hGdHt8J2ycA
Full map can be found here: http://matrieux.dk/downloads/MatrieuxSurvivalS4.zip. the chest is right at the spawn point

What I expected to happen was...:
Nothing really...

What actually happened was...:
The top of the chests dissapered (see picture)
And my skin bugged when looking in third person mode

Steps to Reproduce:
1. Spawn a spider
2. Throw a invincibility potion on the spider.
3. Place a chest next to the cage.