Section 6 "Approximation" erroneously claims that results of Raghavendra apply to VCSP. In fact, Raghavendra's results [75,76] are about *maximisation* version of the problem, where one additionally assumes that all functions take values in [-1,1]. Similarly, the claim that Max-CSP is equivalent to a certain VCSP is true only when one considers optimisation to optimality, while approximation properties of the two problems may be different.
Generally, it is well known that the approximability of maximisation and minimisation versions of a CSP can differ considerably. For example, there are VCSPs that are not constant-factor approximable (see a paper by Dalmau, Krokhin, and Manokaran on this subject).