First of all Cichlids are part of the order Perciformes, that is, they are perces.
Perces are one of the few orders wioth both sweetwater fishes and seefishes.
Cichlids are, apart from being freshwater perces distinghuished by a singular nostril (in stead of 2) on each side of the body, and an disrupted lateral line system.
This system informs the fish about watermovements, enabling it to detect swimming animals, such as predators, or pry, but also signalling from, say, parents.
Normally fishes have some on their head, and a line going backwards. Cichlids have this line interrupted, the first part bends up, I think to detect signals from parents, the second part did remain in place.
The congo tetra, something interruptus, is the only other fish, non-cichlid, with such an interrupted (hence the species name) lateral line.
You already mentioned cichlid teeth. As far as I know, more fishes have pharyngeal teeth, but cichlids have the supporting bones connected with each other, enabling them to use much more force, and controlled movement.Related families have them as well, but these are not freshwater fishes.
This is a true feature, but hasrd to note on life fishes, or in a tank
Antorhe feature of cichlids is their caring for youngs, but againl other perces have breedingcase as well, but, the only female fishes I know which perform care for the young are cichlids, and I only know chichlids as true parents, Anabantoids, for example, stop their involvement when the fry swim. Cichlids breed much, much longer (I heard Crenicichla of 15 cm being protected in some cases)