A synovial basal joint. A synovial joint is basically a joint between bones with a fluid-filled cavity between them - a good example might be your jaw joint. The basal joint is between the pterygoid (a bone of the palate) and the basipterygoid process of the braincase. Pretty much all dinosaurs have this--and so do many modern reptiles and birds with both kinetic and akinetic skulls.
A synovial otic joint. The otic joint is between the squamosal (a bone of the skull roof) and the quadrate (a bone of the jaw joint). Again, pretty much all dinosaurs, and many kinetic and akinetic modern animals, have a potentially mobile otic joint.
Protractor musculature. These muscles attach to the bones of the basal and otic joints (and you need to move those bones for kinesis), but the muscles are present even in modern taxa with akinetic skulls (e.g., the tuatara). These protractors apparently varied in size across dinosaurs.
Kinetically permissive linkages. This is a fancy way of saying that the skull is set up to allow movement (aside from the otic or basal joints). In modern animals, this takes the form of thin and flexible bones (as in the snout of some birds), missing bones (as in the loss of stabilizing cheek bones in lizards), and the addition of extra synovial joints, among other things. All modern animals with kinetic skulls have these--and dinosaurs lack them, in Holliday and Witmer's view.