Discount coupon causes parse error

I have added a discount coupon in then admin area. When I enter the coupon in checkout i get the message:

Oops, something went wrong (parse error). Please try again.

How can I analyse what is the problem here?

This can be difficult. The message means that the response from an AJAX request is not HTML. There is probably an error, warning or notice message embedded in the response. You can look at the response in firebug (or similar) and you can check your PHP error_log files to see if there are any errors reported. Rarely (but occasionally) you can see the problem from a “view source”. But usually you're going to have to go look at the DOM for the offending container that the AJAX is trying to replace.