Did I hook up this CD4052 Analog Multiplexer correctly?
Your input logic to A,B should use the V1 voltage (12v) for a high, not 5v.  

See page 7 of the data sheet for VIL, VIH.  

For example, it shows that with Vdd at 10v you need at least 7v for a high.  So at 12v Vdd you may need about a 9v minimum. 

(Also see the switching limitations listed by jms.)