Mourad Bakhali has a cool guide that explains how to bring the good old times.
Games from PS1 had this specific shaky and wobbly effect of vertices which was caused by the lack of floating-point precision. How does one recreate that effect in UE4?
The developer pointed out the hardware part of PlayStation only allowed fixed-point calculation "so when the camera is moving or an object is moving, any given vertex stays in its position until it’s close to the next position and suddenly snap to it".
The full guide will explain to you all the parts, including materials and more. Everything is documented, so you'll figure out the tricks in no time.
Find the full tutorial here.