As Mike said above, and can be seen from closely inspecting the photos, the rod threading is more worn in the center region than the ends. The nuts, new and old, demonstrate notably more play when at the center of the rod than at the ends. While the center even looks to be less in diameter, it measures equal in diameter; it is the width of the threading that has been degraded through wear.
The question now is do we want to attempt replacing the worn acme thread rod with new? The rusty rod in the photo is not worn, only has superficial rust. It can be just fine with a rust clean off and oillng, I believe.
Also, the closs slide can be anticipated to have at least as much of the same issue as the topslide. Beyond that, the Bridgeport has a tremendous 50+ mils of backlash on the X axis, about 30 mills on the y axis. Determined by checking the travel of the wheels with the deck locked.
While we are at it, lets order a drum of anti backlash filler.