Yesterday I set the Near Clipping plane to 0 in Blender, and it sort of did the same thing. Turns out setting the Near Clipping plane to 0 causes all kinds of issues.
Yes, Setting the near clip plane to 0 is not something that you should do. You always need to have a value for the near clip plane, otherwise, all things that get mapped to Z are set to 0, which causes the issue.
Barring the 90’s feel of the web page, this is a good resource of information about the Z-Buffer and your Clipping Plane. Learning to Love your Z-buffer.