Causes of obesity were more complex than Smith stated, the report said
Stars make "misleading claims" about science - and their unproven opinions then "travel widely", a charity warns.
TV cooks Delia Smith and singer Mariah Carey were among the entertainers criticised by Sense About Science.
Smith said obesity could be "cured" if people "cut down sugar addiction", but scientists said this was impossible.
And Carey's grasp of maths came under fire after she said her album E=MC2 stood for "emancipation equals Mariah Carey times two" - rather than squared.
Smith said "addiction" caused obesity, adding: "After six weeks [without sugar] everything will taste sweet... because you will have got your palate back to what nature created.
"We could cure the nation if we cut down sugar addiction."
But Lisa Miles, who is the senior nutrition scientist at the British Nutrition Foundation, responded by saying: "You'll never get rid of sugar from the diet, nor would you want to.
"You consume sugars naturally in many foods, such as fruit and milk, which provide us with important nutrients.
"Also, the causes of obesity are much more complex."
Mathematician Dr David Leslie said Carey had "misread the algebra" after adapting Einstein's famous equation for her album title.
"The 'two' in the equation means C squared, not MC multiplied by two.
"The correct reading of the equation is E=MCC, so perhaps Mariah's re-interpretation should have been 'emancipation equals Mariah Carey Carey'?"
The charity's report also criticised Hollywood actor Tom Cruise after "an old video of his views about psychiatry was leaked" this year.
"Psychiatry doesn't work," Cruise said. "When you study the effects, it's a crime against humanity."
But Harriet Ball, who conducts psychiatric research at King's College in London, said a range of treatments, including drugs and Cognitive Behavioural Therapy, had been "shown to be effective".
Actress Demi Moore was criticised for misunderstanding blood toxicity and saying she had been using "highly-trained medical leeches" to "detoxify her blood".
"They have a little enzyme.. and when they are biting down on you, it gets released in your blood," she said.
"Generally you bleed for quite a bit - and your health is optimised. It detoxifies your blood."
Demi Moore had failed to grasp the detoxifying process, the report said
But biophysicist Dr Daniella Muallem said: "For something to be detoxifying, it should remove toxin. Even if your blood does contain toxins, simply removing a little bit of it isn't going to do any good."
Ellen Raphael, the UK director of Sense About Science, said she did not expect people to know "everything" about science.
"The problem comes when they don't consider checking it or asking a few questions before they speak out," she said.
"With the internet and 24-hour news, media celebrities' misleading claims travel widely.
"They add disproportionately to the stock of misinformation that we all then have to wade through to make sense of a subject. A little checking goes a long way."