I did not see the program, but I have been following the subject for almost 50 years. Mars and Mercury both have a bit more than 1/3 the surface gravity of Earth. We typically suppose that this will not have the bad effects on humans that mico gravity has, but this has not been tested long term. Our technology is presently far short of being able to terraform Mars. Modest advances will permit habitats that are far from self sufficient on Mars and on asteroids, but at incredible cost.
Making Mars exactly like Earth, may remain impossible for thousands of years. A step in that direction is called a statite = a giant mirror sort of in orbit around Mars. It is positioned to send extra sunlight and heat to the surface of Mars, and make the days at least a bit longer than the nights. This provides closer to the optimum amount of light for photo synthesis and increases the average temperature. Statites are a variation of the solar sail, but in one square mile size, they rarely deliver the light exactly where it is most needed and no light is delivered to Mars part of the day, even with considerable fuel consumption. Warmer means more volatiles enter the atmosphere from the surface. Perhaps enough for some Earth type vegetation, but probably not enough for animals or humans.
In my opinion neither nuking Mars, nor adding green house gases other than water vapor is good.
Far in the future it may be practical to deliver more volatiles to Mars by changing the orbit of comets so they hit Mars. Neil
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