Hi Jnlbauer,
Thanks for visiting Apple Support Communities.
If you're seeing unexpected behavior with FaceTime and AirPlay, first make sure your iPad is up to date (iOS 7.0.4 was recently released.)
- Ensure your device is connected to a power source. To avoid potential data costs connect your device to a Wi-Fi network.
- Go to Settings > General > Software Update. iOS will automatically check for available updates. Available updates download automatically if your device is connected to Wi-Fi and a power source.
- If an update is available* you can tap Download to download the update.
- After the download has completed tap Install to update your iOS.
See this article for more details about updating your iPad:
iOS: How to update your iPhone, iPad, or iPod touch
http://support.apple.com/kb/HT4623
If the issues persist after updating, see these articles for more troubleshooting tips:
iOS: Troubleshooting FaceTime
http://support.apple.com/kb/ts3367
iOS: Troubleshooting AirPlay and AirPlay Mirroring
http://support.apple.com/kb/ts4215
Best Regards,
Jeremy