Since pterosaurs (and other tritosaurs) nest between rhynchocephalians and squamates, there are a few traits they likely shared based on phylogenetic bracketing (unless specifically excepted based on fossil evidence). According to Evans (2003) these include:
(1) A derived skin structure with a specialized shedding mechanism involving distinct epidermal generations that are periodically lost and replaced, linked to
a cyclic alternation between a and b keratogenesis. — Ttritosaurs had scales. Pterosaurs also had pycnofibers, hair-like structures that first appear in Sharovipteryx. Unfortunately there is no evidence of skin shedding in any fossil lepidosaur.
(1A) The possession of a crest of projecting scales along the dorsal midline of the body and tail may also be unique to members of this group. — this reaches its acme with the tritosaur fenestrasaur, Longisquama.
(2) Paired male hemipenes housed in eversible pouches at the posterior corners of a transverse cloacal slit. These hemipenes are well developed in squamates and rudimentary in Sphenodon. — the fossil record does not include such structures.
(3) Notching of the tongue tip, possibly in relation to the development of the vomero-nasal system. — Barely notched in Iguana. I don’t see this in known rhynchochephalians or tritosaurs based on the division of the choanae into anterior and posterior fenestra, which appears in basal scleroglossans only.
(4) Separate centres of ossification in the epiphyses of the limb bones (a condition acquired independently in mammals and some birds). — This has never been noted in tritosaurs.
(5) Specialized mid-vertebral fracture planes in tail vertebrae to permit caudal autotomy facilitated by the organisation of associated soft tissue. — This has never been confirmed in any tritosaur, but then again, they are rare as fossils.
(6) A unique knee joint in which the fibula meets a lateral recess on the femur (not end to end as in many tetrapods) — This must be a very subtle trait. I see this trait in Tupinambis, Varanus and Bahndwivici, but not in very many other lepidosaurs.
(7) Specialized foot and ankle characters including a (a) hooked fifth metatarsal, (b) a specialized mesotarsal joint with a fused astragalocalcaneum and (c) an enlarged fourth distal tarsal. — (a) The hook comes and goes. In basal rhynchocephalians, not present. It is present in Sphenodon through Mesosuchus, starts to fade with Rhynchosaurus and is gone in Hyperodapedon. Something of twisted fifth metatarsal present in most tritosaurs. Minor hook in basal squamata, becomes larger in Varanus, absent in snakes and other limbless lizards, of course. (b) In tritosaurs no ankles are fused except in drepanosaurs. (c) Also large in tritosaurs.
(8) Other soft tissue features include a sexual segment on the kidney; reduction or absence of the ciliary process in the eye; presence of a tenon (cartilaginous
disc) in the nictitating membrane and its attachment to the orbital wall. — These have never been observed in any lepidosaur fossil. But that doesn’t mean they weren’t there.
(9) In addition to these characters, all lepidosaurs show one of two kinds of tooth implantation, pleurodonty and acrodonty. — Basal tritosaurs have pleurodont teeth. Macrocnemus and later tritosaurs have thecodont teeth that happen to be much larger.
Part 2 is posted here.
Evans SE 2003. At the feet of the dinosaurs: the origin, evolution and early diversification of squamate reptiles (Lepidosauria: Diapsida). Biological Reviews, Cambridge 78: 513–551.