Concerning the whole Squamata phylogeny : the Pyron et al. cladogram is not the first to reveal such evolutionary relationships, in fact the examples that you give (Cordylidae - Scincidae; Agamidae-Chamaeleonidae) are very old groupings (or slightly more recent for Amphisbaenia-Lacertidae). So even if the results of convergent evolution can sometimes be striking (e.g. Platysaurus), none of these relationships are really shocking.
If these can sometime appear a little odd to some of us may be due to the fact that the most recent phylogenies are rarely used in general works either by conservatism or by convenience ( which book dealing with reptiles include birds as well??). Especially paleontologists tend to stick to the old classification (with Iguania being the most basal clade) even in higher level publications.
Concerning the Algyroides-Dinarolacerta relationship: even if this paraphyly of Algyroides has been suggested by multiples analysis (Pavlicev & Mayer), none was sufficiently significant to act the inclusion of Dinarolacerta in Algyroides (or the Algyroides split)!
Pavlicev M, Mayer W. Fast radiation of the subfamily Lacertinae (Reptilia: Lacertidae): history or methodical artefact? Mol Phylogenet Evol. 2009 Sep;52(3):727-34. doi: 10.1016/j.ympev.2009.04.020. Epub 2009 May 8.
Platysaurus: