There are a couple reasons why your GCM API key was rejected when entered into Mixpanel. During the setup process, first make sure that you are correctly creating a Server Key (not an Android Key), and pulling the correct GCM API Key value.
The second and most common reason for the API key failing is due to IP whitelisting. In order to use your Server Key in conjunction with your Mixpanel project, we require that you don't add any whitelisted IPs to your Server Key upon creation.
Leaving the IP blank allows all IP addresses to access your Server Key via the API key, whereas whitelisting a specific IP will limit the access to only the whitelisted IPs.
If you are still having issues, don't hesitate to email us at firstname.lastname@example.org.