When knocking pteranodons out, be sure to have a bola, it doesn't take many tranq arrows to knock it out. Once it is down, put spike walls up around it (with a little space so you can go in and out) so it doesn't lose taming efficiency or die.
To kill pretty much anything on these birds, tame a high level, then pump stam to 3k, then the remainder in melee. Barrel roll into alphas etc. But keep eye on Stam. Never regen Stan on ground, know your ledges!
Since the bird nerf, these things are not near as useful. Still, if you get one level up stam and a bit of weight. This is so you can fly across an ocean without running out of stam and dropping into a pool of jellyfish to have your butt hair zapped off.
Be sure you whistle (follow) when riding your tame. If you accedntly jump off or get saddle jacked off your bird, he will follow you to the ground and you will have a better chance to recover your tame.
If one were to tame a low level pteradon, it should be put to use as a travel bird, nothing more, for it is too weak for anything else. However. High level pteradons are excellent for fighting, kibble tamed 100+ can be used to kill alphas, in packs, or alone in niche cases.