How often does the Mertens function vanish?
Quoting an answer to the question https://mathoverflow.net/questions/273845/oscillation-of-the-summatory-möbius-function
Let $c=14.1347251…$. Then there are at least $(c/\pi-o(1))\log y$ sign changes in $M(x)$ in the interval $[1,y]$. This was proved by Kaczorowski and Pintz (Acta Math. Hungar. 48 (1986), 173-185, doi 10.1007/BF01949062).
This may well be the state of the art, but any comments on further results would of course be welcome. If no more is known then this question is a duplicate of the linked question.