Operating system and graphics card
NVIDIA GeForce GTX 660
Worked: same error on offical release 2.78
Short description of error
bevel modifier (bevel by weight) creates an unwanted UV-gap at a vertex with 5 edges connected. 2 edges has bevel weight. Error visible if bevel modifier is applied of if subdiv modifier is active. The UV-gap disappears if 4 out of 5 edges has a 90 degree angle to one another.
Exact steps for others to reproduce the error
Based on a (as simple as possible) attached .blend file with minimum amount of steps
Hard to explain how to model. Easiest for you is to open the .blend and test it. I put a shape key on the "error mesh". Turn the shapekey on/off to show the error.