Google announced today that it has updated its Google Mobile iPhone app to push notifications from users' Google accounts to their phones. Now, an icon badge will show when you've got new mail in Gmail or when a reminder for a Google Calendar event comes up. The badge will appear right on the home screen. "We've also added spiffy features to get you information faster -- when looking for flight info, weather, stock quotes or currency conversion you'll see answers before you even hit 'Search'," says Google engineering manager David Singleton.