On OS X Lion:
- Choose System Preferences from the Apple () menu and then click MobileMe.
- Disable MobileMe.
On OS X Mountain Lion:
- Disconnect the computer from the Internet by either unplugging the ethernet cable or by turning Wi-Fi off.
- Open Aperture.
- A warning that the MobileMe password is incorrect will appear. Click Cancel.
- After Aperture opens, quit Aperture.
- Relaunch Aperture. A dialog indicating MobileMe has been discontinued will appear. Dismiss the dialog.
- Re-enable your Internet connection.