Instruction for the AVIC-X850BT has me connecting the pink (car speed signal input) to the vehicle's speed detection circuit for the navigation to be accurate.  How bad will the navigation be if I don't do this?

Hello, Well I had mine disconnected because BestBuy did not feel it was necessary. It is necessary because it helps give accuracy to your position on your Navigation and it is more precise when reading the speedometer from your car's computer. It also helps maintain your position on the Navigation map when you are within tunnels and such. So if you get the chance, definitely connect it. Also don't forget the Illumination wire. This one dims your head unit's brightness when your turn on your headlights, if not you are going ot have to dim it manually every time you use the car at night. It is very bothersome.