This question and answer helped me solve a specific problem with signing up new users in Parse.
Because the signUp( attrs, options ) function uses local storage to persist the session, if a user is in private browsing mode it throws the "QuotaExceededError: DOM Exception 22: An attempt was made to add something to storage that exceeded the quota." exception and the success/error functions are never called.
In my case, because the error function is never called it initially appeared to be an issue with firing the click event on the submit or the redirect defined on success of sign up.
Including a warning for users resolved the issue.
Parse Javascript SDK Reference https://parse.com/docs/js/api/classes/Parse.User.html#methods_signUp
Signs up a new user with a username (or email) and password. This will create a new Parse.User on the server, and also persist the session in localStorage so that you can access the user using {@link #current}.