Of American-English origin, the phrase teeth like stars is applied to false teeth, the image being that they ‘come out’ at night.

This phrase is an ironic use of the clichéd image of teeth shining like stars—clichéd image occurring, for example, in the following advertisement published in The Evening Star (Washington, D.C.) of Wednesday 27^th September 1893:

Shine Like Stars.
If you would make your teeth shine like stars and a real ornament to your mouth, use LISTER’S DENTIFRICE—also purifies the breath. 25c. bottle. For sale here only.
Thompson’s Pharmacy, 703 15^th St

The earliest occurrence of the phrase teeth like stars that I have found is from The Evening Star (Washington, D.C.) of Saturday 28^th August 1897:

A Friendly Suggestion.

From Scribner’s Magazine.

He (dreamily)—“By Jove! her teeth are like stars!”
She—“Because they come out at night, you mean?”

The second-earliest occurrence of the phrase that I have found is from The Cream Of our Exchanges, published in The Boys’ World. Published In the Interest of the Young People (Wichita, Kansas) of Saturday 9^th April 1898:

Primus—“Her teeth are like stars”
Secundus—“Because they come out at night.”

The phrase was borrowed into British English; the first occurrence that I have found is from The Sporting Times (London, England) of Saturday 3^rd February 1906:

Young Hopeful: “Grandfather, why are your teeth like stars?”
Grandfather: “Because they shine, eh?”
Y. H.: “No. Because they come out every night.”