So it turns out that the whiz-bang gadgetry of the modern television set may not be the best way to watch a movie.
The fellow at the link goes into some great detail, but the upshot is that TV sets in the store are set to grab your eyeballs. The settings which grab your eyeballs are not the settings which are best for watching a movie. Colors will be too bright, outlines too distinct, the blue balance will be too heavy, and so on.
And LCD screens, which are the most common kind of flat-screen televisions sold today, have inherent flaws which fine-tuning and optimizing can't cover up.
So it may be awhile before I send my old set out to pasture. I may wind up watching more movies on the iPad at the gym than I do on my set, but at least I know when I watch it on my set I won't cut my eyeballs open on the red-green contrast setting.