In later episodes, Nash has a very strict rule about no eating in the Cuda. While it could be argued that he simply became more strict later on, is highly unlikely that Nash would allow Harvey to eat noodles in the Cuda let alone have Joe order cherry pie for someone in handcuffs that could easily stain the white interior.
Despite the common trope of government bureaucrats making silly mistakes, it is highly unlikely that someone would be forced out of retirement due to a clerical error. Or that the error could be "negotiated" to a lower number of days required to work to regain the pension.
A 20 year veteran of a law enforcement agency would know what VIN stands for.