One problem I can see is that the emoji from SMS and the emoji from the web page can look quite different.
Thanks for the feedback! Under the hood Authmoji displays unicode, so it depends on the OS you're using. It should not be a problem if you enter the emoji sequence from the same phone you receive the SMS. We've also selected a subset of emojis that are very closely matched across OS. If you see any major discrepancies, please let us know!
Authmoji adds a fun spin on two factor auth and one time passwords by using emojis instead of numbers. We just launched, so let us know what you think!