Server environment is CentOS 7.2 and client environment is Windows 10 x64.

The process for submitting a bug to mojang is basically the same as it is here, except you post on bugs.mojang.com instead of here.

Looks like there already is a report there: MC-54026. I've attached your world to it though since it didn't have clear reproduction steps. Thanks!

World with example contraption provided. It may be necessary to increase the height of the thing to get it to bug out. I've only ever seen it occur on the way down.

There is a button on the bottom for it to go up as well as at the top to make it go down. Movement is triggered by block updates so if you do something to block its path and it stops moving, just place and break a block near the BUD switch and it will start moving again.

The player who built it says that it also occurs in single-player mode which suggests that it's a client-side bug. I don't mean to shovel this onto you guys necessarily but I don't know the procedure for submitting a bug to Mojang and would appreciate it if someone more familiar with the process would take it further.

bug_world.zip

Piston block motion performed entirely clientside (though it's separately done serverside), which is how it's possible for this to happen. Though getting a world to cleanly reproduce this would be helpful.

A world, build it in a flat one.

Attach it how? As a world? As a schematic?

We don't take video bug reports because they are even harder to understand.
Please build the minimal contraption required to reproduce this issue and attach it to this ticket with instructions.
Also compare to Vanilla and make sure you are not running any plugins.