I installed and applied for the dongle yesterday. It's pretty quick and painless--the credit check is a little much, but if it keeps the quality high I'm ok with that. Plus, this service is just too damn cool to pass up.
How could the credit check keep quality high? It's not going to change who I can accept payment from since the payer doesn't have any connection with Square. Square isn't lending me any money that I somehow need to pay back when I accept a payment. So... why check my credit again?
My understanding is that they use it to verify your identity and it's also used to set your daily and per-transaction limits. My guess is that this is just fraud prevention and a way Square can keep scammers off their service.