Movement glitch not present before latest PS4 system OS major update to v5 (currently have latest v5.01 installed)...
Started playing through TLOU Remastered (digital download, v1.09, latest from what I can see) after seeing second trailer for TLOU II. Noticed significant movement glitches where playable character doesn't move smoothly & consistently corresponding to actions on the movement stick. Particularly problematic while stick is pressed forward and is shifted slightly left or right for gentle strafe motion to avoid obstacles & such while moving; also, the transition between walking & jogging is very unpredictable, leading to inconsistent movement speed. Glitch is not present in any other games, including other Naughty Dog titles (entire Uncharted series on PS4).
Tried swapping movement sticks; did "fix" the problem, but a.) not at all used to that stick config, so that renders the game nigh unplayable; and b.) wasn't an issue before latest major PS4 system updates (v5), leading me to suspect the issue is related to system software conflicts rather than an issue with hardware.
If swapping sticks resolved it, it means you have worn control inputs on one of your controller thumbsticks. The system update wouldn’t be related.
As a hardware issue, we’d recommend swapping out the controller.
Sorry we can’t be more help.