Sounds like he either accidentally left off a ground connection or ended up shorting something and blew a fuse. Why does he think he didn't blow a fuse? Has he tried disconnecting the work he did, replacing any fuses associated with the instrument cluster and/or speed sensor, and then seeing if the instrument cluster is back? Is he knowledgeable enough to use a volt meter to trace the power interruption?
If the speed sensor is one that communicates with the car's transmission computer, it would be reasonable that you would have transmission/shifting symptoms. Has a dash warning light come on yet? Usually takes a few drive cycles. If it has, he should have a shop use a Nissan equivalent tool to access codes (I don't recommend what we call a generic scan tool in this case because it might not pick up on a transmission code).
I would not assume that the instrument cluster itself is the problem. I recommend looking on the Car Talk website or the iATN website to find a good independent repair shop in your area. Pay them to do up to an hour of electrical diagnostics if your DH can't figure it out soon. Have your husband explain exactly what he did when hooking up the radio.
By the way, most GPS have an internal method of calculating speed. Did the installation instructions tell him to hook into the car's speed sensor?