Inspired by Michaela D's comment, I wanted to add another gadget to the list - a smart mouth-washing liquid.
To detect abnormalities not visible by a camera (back of the teeth, nonvisible changes on the surface of teeth,
To clean mouth more efficiently
To give recommendations about the brushing technique
To give information about present tooth fillings
You would simly wash your mouth with the liquid for 30 seconds by thorough gargling. Liquid would leave a blue trace on teeth. After this, you would wash your mouth with water for 30 seconds. Water would rinse part of the blue trace from the teeth. The colour would still be present on hard-to-reach places, cavity, dental filling holes, damaged tooth enamel or teeth, etc. You would then follow instructions on how to take photos of your mouth from inside using gadgets mentioned in the idea text. After taking photos, you would rinse your mouth with water and the colour would dissapear. Smartphone app would do the magic and tell you what you should do based on the health of your teeth.
The "magic" recipe of the liquid
The main thing in the liquid should be a chemical of colour that reversibly binds specifically to dentin. Every damage of enamel exposes dentin and that's what this method would use to give you more information about the health status of your teeth. The chemical could be similar to dentin bonding agents or could be an antibody that binds to dentin. I need to work on this for a bit more.