I just received an email from Nikon USA indicating that there is a potential issue with Nikon D750 DSLR cameras manufactured between December 2014 and June 2015. As described here, the issue affects the camera shutter and can cause shaded images.
Check your serial number here. If your camera is affected, Nikon USA will provide you with a free UPS shipping label to send the camera in for service.
Interestingly, my Nikon D750 is indeed included in the list of affected cameras. I’ve not seen anything indicative of the shutter issue in my use. Nevertheless, I will be sending in the camera for service. I encourage anyone with an affected D750 to do the same; if for no other reason than to have the peace of mind from knowing your camera has been serviced.