Sarnak's conjecture from 2010 states that all zero entropy systems are Möbius disjoint. The celebrated Chowla conjecture on autocorrelations of Möbius function implies Sarnak's conjecture, and, by a recent theorem of Tao, the logarithmic version of the two conjectures are equivalent. However, also positive entropy systems can be Möbius disjoint. We will be discussing uniform (in $x\in X$) convergence in $(*)$, show that the seemingly stronger requirement of uniform convergence in $(*)$ for zero entropy systems is equivalent to Sarnak's conjecture, and show (under Chowla conjecture) to which extent uniformity fails in positive entropy systems.