Slow notifications delivery:
In some cases it can take some time (even several minutes) to deliver Google Cloud Messaging (GCM) notification to the device. This is because of GCM system architecture: "To prevent abuse (such as sending a flood of messages to a device) and to optimize for the overall network efficiency and battery life of devices, GCM implements throttling of messages." (GCM Advanced Topics)
After manual app installation GCM no longer works:
If you are installing your application manually on the phone you may need to delete previous installation of your app first or increase android:versionCode in your Android Manifest. When you update your application with the old version code the GCM token will not be updated. That will prevent notifications delivery.