When I use

1. fill(col, alpha);
2. rect(0, 0, width, height);

at the beginning of the draw() to get a blurry/trace effect, I've always had issue with alpha values under 32.
Does anyone know why?

try this, then change the value of alpha with a lower one and look close a little from below...

1. int op = 32;
2. 
   
3. void setup(){
4.   size(200, 200);
5.   background(255);
6. }
7. 
   
8. void draw(){
9.   fill(255, op);
10.   rect(0, 0, width, height);
11.   fill(0);
12.   ellipse(random(width), random(height), 10, 10);
13. }