How can I mirror my OS X screen and functionality to an Android tablet?

OS X has a built in VNC-compatible server (This is for 10.9, older versions have it but I'm not sure if some earlier ones have the controls somewhere else):

1. Check System Preferences > Sharing > Screen Sharing

2. Click Computer settings… > VNC viewers may control screen with password: (set a password)

3. Setup an ad-hoc WiFi connection between the tablet and the laptop: Click Create Network… from the Airport menu and connect to it from the tablet.

4. Using a VNC client on the tablet, such as: https://play.google.com/store/apps/details?id=android.androidVNC&hl=en, connect to the laptop using the Bonjour address and the password you set above—Back on the Screen Sharing page, it will say something like Other users can access your computer's screen at vnc://mdryden-mbp.local.

With any luck, the laptop's screen should appear on the tablet and you'll be able to control it. I haven't tried the app above, but many tablet VNC clients can be configured to both move the cursor and click upon tapping, or else have a virtual trackpad on screen.

I was doing some research for a different but similar request as this and ran across AirDisplay from Avatron Software. (I am not affiliated with them in any way)

It allows you to extend your desktop to an iOS or Android device. What's really interesting is that it allows you to interact through that device.

So, you could have that particular navigation app running on the extended display (the tablet) and you could still interact with it. I am testing their software to extend a Mac to a display running Windows and so far, it's working well. They have free trials for tablets, too. The price is reasonable at $20