Build and Run the attached project on WebGL.
Click on the options indicated in https://gyazo.com/ede02c8e26743a85980e88f21e98dfa1.
Notice that the buttons backgrounds are only rendered half way through. In Editor and Standalone build, the buttons look fine

In Unity 5.2, this looks even worse, with the text on the buttons being all messed up.
Also reproducible with Unity 5.4.0b8

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The problem here is that NPOT sprites with mipmaps are currently not handled in WebGL. The workaround until this issue is fixed is to disable mipmaps for the sprites.