I was once shooting some road photos on the Garden State Parkway in NJ when I noticed that the photos of the VMSes did not come out! You would see partial lettering and missing spots in the wording.
Ditto for when I photographed the Racetrac Gas Station display near my home, as some of the prices were not all there.
I emailed a friend to ask him what is up and he told me the shutter speed was faster than the electronic digits being displayed both on the Parkway and in the station. In other words the camera was not synced with the display icons and just like photographing a flashing traffic signal, you also could snap the shot in between flashes making the signal look like its out completely or caught while in the amber mode to change or even a red light if you photograph the red flasher.
Now what I do not understand is from the naked eye perspective is those displays are on constantly and there is no flashing of the icons. Or is it really flashing at thousands of a second intervals so fast that we cannot see it happening while the camera can? This seems so odd.
Yes, that's what's happening. If you slow your shutter speed, the sign will be more legible, but you can't really slow your shutter speed too much from a moving car without introducing motion blur into the photo.
Same thing happened often trying to take a picture of a TV screen.
The naked eye is kinda slow, but adapts much easier than an electronic eye, such as in a camera.
Some photos of the LED variable message boards tend to appear really fouled up during faster exposures.
(https://farm6.staticflickr.com/5813/30506885454_94b3f694d5_b.jpg) (https://flic.kr/p/NtMLcG)
You might fare better by shooting from an angle, but that cannot be achieved while driving towards it.
Usually I just notate what the VMS said in a highway photo album if it's relevant. I've had some luck trying to shoot from an angle off on the shoulder but that isn't something you'll get a chance to do on a freeway.