I'm trying to simulate a retro cartoon look with large halftone dots something like this:
Does anyne know where I can download an Illustrator pattern like that?
You don't need to download it; you can easily create a [pattern] of dots that look exactly like the example.
This may help:
A dot pattern is about the easiest pattern to make.
Draw a round dot.
Draw a no-fill no-stroke square and send it to back.
Select both and drag to Swatches palette.
Fill a shape with the pattern, scale and rotate pattern without scaling or rotating the shape.
(de-check Objects in the Scale and Rotate dialogue boxes.)