I always look at these things from an embroidery point of view. We like simplicity. Why? At some point someone is going to want this as a left breast logo. Complicated stuff with 1/32 inch lettering sux.
From that standpoint it looks ok.
I'm in the same boat as binki when it comes to looking at everything from an embroidery stand point ("simplicity" just depends on the pattern and what is needing to be done within the given design) .
However, that double contour outline is going to be an issue. Particularly the outer one as it is smaller. Sizing at 3.5" (typical logo crest size, although anything up to 4" would work, but 4" can be pretty big depending on the pattern), that outer contour is coming at .02" width. Some machines (not all) will struggle with that trying to do a satin stitch, even with slowing the machine down, putting in a smaller needle and lighter weight thread. Depending on what fabric you are putting it on, might not turn out so well (due to push/pull of the fabric as it interacts with the needle and thread). Make that outer one a running stitch (or bean stitch, stem stitch etc) and it just doesn't look good against the first satin outline, but it would be more appropriate for the size (width) of that outer contour outline.
I tend to advocate against double contours (or more) for that very reason (although I do have other reasons why I'm not too fond of them in embroidery).
The detail definition work can also be an issue with it's close proximity to the first outline, but you do have a couple of options with it, one of which most don't think about doing, but one that I like to use.
I don't know how well it would convey size of everything uploading here, but I did include a screenshot of the picture in my program sized at 100%. My program is calibrated to that particular monitor, so that is 1:1. The rectangle itself is 4" tall, but the design is ~3.5" tall (I think 3.48", close enough)
I know you said it was designed for 2 color screenprint and graphics, but (like binki said) typically sooner or later they get to embroidery, if not for shirts, then for hats (that would open up a whole other can of worms, size may or may not be the issue, depends on the style of hat and the machine being used).