I ran into an error and tracked it down. It looks like using [wp-legacy-stripe] to get the form inline on the page (rather than in the iframe) does not work in 1.4.0.
After hitting the submit button I would get a long pause and then an error message on the page: "There was an error processing your card" And in the browser's error console:
Error: ReferenceError: ajaxurl is not defined
Source File: [domain omitted...]/wp-content/plugins/wp-stripe/js/wp-stripe.js?ver=3.4
I looked into this and it seems that the newer ajax code does not yet work with putting the form directly on the page via [wp-legacy-stripe].
This is too bad because I like having the form on the page, and the iframe/pop-up is actually appearing *behind* my header in the default Twenty Eleven theme. (In that theme the header#branding CSS is set to z-index: 9999;)