I don't think a "Continue" button is the worst offense in this flow - a lot of authentication screens keep their next step vague, and use "Continue" or "Next". I think the main problem is that when the email address isn't found, you're immediately dumping the user into a registration flow.
Error recovery is a standard UX heuristic that states that when the user makes a mistake, they should be told what happened, and how to fix it. The user tried to log in and wasn't successful. They need to know what happened, and be given another chance to try again (unless you're, say, cutting them off after 10 bad attempts for security reasons). Immediately having them sign up with a potentially mistyped email invites an account to be created with an email that isn't real.