What is correct one less thing to worry about or one thing less to worry about?

Both are ok, but the first phrase is colloquial (not to say incorrect) because "less" is properly used only of quantities that cannot be counted. The technically correct Word, in the first phrase, is 'fewer.' There is also a difference of meaning in the two phrases. In the first case, less is an adjective modifying thing; in the second, it is a noun. The second phrase could be restructured thus: Less to worry about, by one thing.

In English the adjective precedes the noun as in 'The green house' whereas in French the adjective follows the noun as in 'La maison verte'. In bilingual countries such as Canada (French/English) you will occasionally find phrases that jump the language barrier and have a French grammar to them, such as 'One thing less to worry about.'