In the published version of the paper:

Martin Bauer, Philipp Harms, Peter W. Michor: Sobolev metrics on the manifold of all Riemannian metrics. Journal of Differential Geometry 94, 2 (2013), 187-208. arXiv:1102.3347. Euclid (pdf).

there is a missprint on:
page 195, line 2: is smooth in $(g,h)$ instead of is smooth in $(f,h$.

The version on Peter Michor's homepage has been corrected.