Princess Nyna, when she finally becomes playable, has poor stats and the worst growths in the game, essentially only being there to be rescued from Medeus, who would eat her if he's low on health. But it does make a bit of sense — she's a princess, and also the last member of her royal family, and thus she simply wasn't trained for combat. Exactly why would you send the last membress of the most royal clan straight into the battlefield, anyway?
A clever case of Gameplay and Story Integration combined with Developers' Foresight - Even Minerva can use the Aum staff, as only a princess can use it. Minerva is indeed a princess, and under normal gameplay wouldn't be able to use the Aum staff... but if she is reclassed to a biship or sage, she can.
In FE1 and FE11, when Marth meets up with Elice and begin the invasion of Doluna, Elice mentions to Marth that the Aum Staff, a staff that can revive the dead, rests nearby and that if Marth lost any companions, it would be worthwhile to grab it. Considering that most players reset when any playable character dies, it makes little sense for FE1 Marth to get the staff, unless he's preparing for the fight against Medeus. His motive for doing so becomes a lot more clear in FE11 where in the prologue, you must sacrifice one of your units as a decoy to keep Marth and the rest of the party alive, and canonically, it's established as Frey. But no matter how hard you try, Frey or whoever you sacrificed cannot be resurrected. This is because in FE12, it's revealed that Frey was merely wounded and left for dead by the enemy army, and is in fact alive and well, and he joins your party in full ready to kick ass.
The original version of FE3 has some hints that the Wyvern Mounts are descended from Insane Manaketes! Brr!
FE12 explicitly states it.
The Avatar from Awakening, which takes place ages after New Mystery, is revealed to look very similar to New Mystery's avatar in a DLC encounter with Marth. Said "new" avatar is destined to serve as Grima's host. What on earth happened to the first avatar to get that kind of a fate pegged on to his/her possible descendent/reincarnation?
In Shadow Dragon's ending, it's stated that Jake and Anna dreamed about visiting far-away continents. Although we don't see Jake per-se, Anna ends up appearing in different continuities in the series as the in-game tutorial person.
Awakening says that all of these Annas are different characters and expies of each other. More exactly, they're from different altenate universes.