From the look of it, it seems like your vertex is over-extending in its bevel size, crossing into another bevel.
If two bevels meet they dont play nicely since they will just ignore each other and 'walk past' one another causing visual glitches like this.
I usually hop into wireframe in such cases and play with the bevel strength value to see which bevel is causing this.
Would be my guess, im a bit rusty though.
I think it was the Clamp Overlap of the bevel Geometry which was turned off... I don't really understand why, but now, it's ok!
Yeah the clamp overlap, that was the name, is there to prevent this from happening.
It is essentially the option ensure that you dont just cranck up the size and have it break the mesh, it will hard limit the bevel size of an edge if it reaches other geometry, though I dont really remember 'how' it works. Like I said im rusty.
But glad you got it working.
