The only thing that comes to my mind is, as Spikey said, scale is not 1, 1, 1, that or in one part of the GIF the bevel is being applied on two vertices and it works well, but the one that the bevel is funky, just one vert is selected. So maybe that drives a weirder behavior.
Also remember you have other options you can tweak in the bevel functionality, changing some parameters usually changes the behavior to what one desires. Try playing around with those.
