CALL TO ACTION BUTTON:
The call-to-action button is important and could be of unusual shapes, but il seems that the email subscription button of Groupon, which, by the way, is essential for him, is peculiar.
Let’s make a comparison first:
The following is the Country-Level homepage, similar for all countries.

The yellow rectangular “Sign up!” is a common & safe call to action button.
However, my doubt is on the City-Level Page if you skip the homepage.

Of course, you could as usual click ENTER after the typing of your email address, but my experience was: when looking at that arrow button, I was expecting a scroll-down menu, or at least something that unfolds, instead of a confirmation message of successful subscription.
CITIES’ LIST:
What does it mean? Well, Groupon presumes that every consumer is subscribed to ONE city’s deals, which is not necessarily true. Take myself for exemple, deals for
- Paris
- Paris extra
- Paris Hauts-de-Seine
- Paris Val-de-Marne
go to my inbox everyday. I admit that it’s of zero difficulty to unsubscribe from the emailing list: just one click, but I’m hoping for a dashbord enabling me to
- have a global view of all the cities I’m subscribed to
- check and un-check any city in a single interface

(Sorry for the ugly illustration, as I’m not a web designer ^^. That would be enough if you get my point.)