Fix for the screen-flickering/spazzing issue when moving:
open the mod folder (<YourUsername>\AppData\Roaming\Factorio\mods\Move with the mouse)
Extract the folder and In control.lua, find this line (walking arrival check):
local direction = get_direction(player.position, config.target, 0.1)
The 0.1 is the "close enough, stop moving" radius, and it's too small — at normal walk speed your character overshoots it every tick, which flips the direction back and forth and causes the shaking/flickering.
Change 0.1 to something like 0.5 (this is what I use)
local direction = get_direction(player.position, config.target, 0.5)
make sure you change the file path from this
mods/move-with-mouse-updated_0.3.4/move-with-mouse-updated/
To this
mods/move-with-mouse-updated/
After that edit the movement is smooth with no flickering. Posting this in case it helps anyone else, especially if you're using this mod for accessibility reasons like I am.