I search the reference for the proof of the following theorem:
Let $G$ be a locally compact group. Then the group $G$ is discrete if and only if the measure algebra $M(G)$ is weakly amenable.
Dales/Ghahramani/Helemskii. The amenability of measure algebras. J. London Math. Soc. (2) 66 (2002), no. 1, 213–226.
is often cited. But it seems to me that the authors only proved the following assertion: $G$ is discrete and amenable if and only if $M(G)$ is amenable.