General relativity I much easier to test in simple systems, like planets traveling in the vacuum, or to get more precision you can test it in the lab https://en.wikipedia.org/wiki/Tests_of_general_relativity . I'm not sure if this is the more accurate current test but from https://en.wikipedia.org/wiki/Pound%E2%80%93Rebka_experiment :

> The result confirmed that the predictions of general relativity were borne out at the 10% level. This was later improved to better than the 1% level by Pound and Snider. Another test involving a space-borne hydrogen maser increased the accuracy of the measurement to about 10^−4 (0.01%).

Nutrition and diets are more difficult to measure (you can't enclose a few thousand persons in the lab for 20 years) and it's full of side effects and interactions. IIRC a low fat diet is still recommended. I think that a better example of the changes in nutrition is the butter vs margarine recommendations, see for example http://www.telegraph.co.uk/news/science/science-news/1179683...