Imitating accelerated expansion of the Universe by matter inhomogeneities -- corrections of some misunderstandings

It is shown that the paper of Vanderveld et al. of 2006 contains a number of logical misunderstandings about the apparent accelerated expansion of the Universe, and about their claim of a `weak singularity': 1. There is no contradiction between Hirata and Seljak's theorem that the deceleration parameter must be positive in ordinary matter and the result of Iguchi et al. that acceleration can be imitated in a Lemaitre -- Tolman model. 2. Even if there were a contradiction, it would not be logically solved by the remedy proposed by Vanderveld et al., which consists in eliminating the so-called `weak singularity'. 3. What they call a `weak singularity' is no singularity at all. 4. Their discussion of the inverse problem is seriously misleading. Along the way, some other errors and misunderstandings are corrected. Most of these misunderstandings recur elsewhere in the literature, so there is a real need to put the record straight.