What is the only characteristic currently known to be unique to all dinosaurs and why is it important

There are multiple characteristic that all dinosaurs shared. Some of the synapomorphies include:
- Vertebrates; skeletons with back bones that surrounds a nerve cord.
- Amniotes; specially adapted for life on dry land.
- Diapsids; two holes located above and behind the eye sockets on each side of the skull.
- Archosaurs; antrobital ferestra, a hole between the nasal hole and the eye socket hole.
But still all of this doesn't separate them from all others, what is unique to them is that all of the 'true dinosaurs' were land dwellers.

As what he you go get the hot dog ; )