Wire size for double pole breakers
It is perfectly within reason to have #12 wire protected by a 30A breaker when the circuit feeds an A/C unit. Depends on the specs of the unit. I would not expect the average home inspector to know this. 

A/C units, welders and electric motors have different rules than the "standard" breaker sizing rules. Things are NOT always as simple as a chart at the home center or a simple electrical book. 

For an air con unit you would typically size the conductors to the minimum circuit ampacity (MCA), and size the breaker to the maximum overcurrent protection (MOP). This is not a hard and fast rule, but it is typical and works for most installations.

It's kind of complicated, but it's all in the NEC, Art.440, Section III.

Here is an excellent overview on Art440 by one of the most respected names in the electrical business, Mike Holt: http://www.dantespeakheatingcooling.com/upload/Mike_Holt_NEC.pdf
See Figure 440-5 and 440-6 in this .pdf for a clear explanation.