Weird rendering on Android: some materials become black, some sprites are replaced

I have a game which looks great on iOS and in editor. However, on Android device the following happens:

  1. I have several 3d objects on scene which use materials with Legacy shaders/Diffuse with texture unspecified. Some of these objects are rendered black while others are fine, the difference is only in color of the material.
  2. The most weird thing: some UI Image textures are replaced with the rendered screen. For example, I have two UI buttons which contain Images as children. One image in button looks fine while other is replaced with a small copy of the whole screen which has a bounding box similar to original image. Both textures for these images have similar settings and no packing tag. I tried to play with publishing settings with no success.

Okay, I fixed it by disabling anti-aliasing in Quality settings (there was 2x multisampling). Another question is, how to use anti-aliasing on old android devices (I experienced these issues on first or second Nexus7).