I have 18" rims as the main tyres.

The compact spare is a 15" rim and the overall diameter (with the tyre fitted) is smaller, so the car will be 'down on one side' should the spare be fitted.

Is this a mistake on the part of Audi?

Maybe worth trying up alongside one of the wheels on the car to compare the overall diameter (with larger tyre on spare possibly?)

Overall size is significantly smaller. Audi dealer claim it's ok. Maybe I should ask another dealer?

Anyone else got a smaller spare than the tyres on their 18" rims? Same size? Perhaps not something you check until you have a puncture!? 

Seems strange that it would be a lot smaller diameter which would mean that the car would steer off in a particular direction because of the difference in ride height, Traction Control would invoke because of difference in rolling diameter, etc.  I would check with another dealer as you suggested