I loved the book and the movie The Martian. And the book went into the science of the potato diet a little bit. But I hadn't heard of it being something people did on Earth.
Just for giggles, I plugged a potato diet into Cronometer.
Typically a good weight loss diet is about 1600 calories a day. And it took 10 baked potatoes to reach that.
at that point you are below the RDA of fat. Not sure if that is a problem on a weight loss diet.
Protein is just 43 g. I think 40 is the bare minimum requirement of protein - so that is probably ok. But there are five amino acids that are below the RDA. I'm not sure if that would present a problem if the diet was kept up long term.
There are a number of vitamins in short supply. B1, B2, B12, Choline, A, D, E, and K. But just like the Martian that can be solved with a multivitamin.
And there are a few minerals that are short. Selenium and Zinc. Plus calcium is really low. So a calcium supplement will be required.
I'm almost sure I could not eat 10 baked potatoes a day for very long - even if I wanted to. Maybe if you could mix it up. Hash browns for breakfast. french fries for lunch. Potato soup for dinner with some potato bread.