For example, VCs with operating experience are great when it comes to sitting down and talking about how to run a business, but sometimes they have less perspective (because their career was probably focused on one or two companies, whereas a professional VC has probably invested in 30+ companies), and they may have trouble keeping their hands off the steering wheel.
A VC with an executive recruiting background can be incredibly helpful at recruiting -- one of the main areas in which a VC can add value (see below).
And a VC who used to be an attorney can be very helpful when you need to get a parking ticket fixed.
Ouch. As a former/ recovering lawyer, even I had to laugh at that one.