-Legitimate Speed Threshold for doubling (4 points)
-Con stat to deal with weight (hey, Axes aren't laughable now!)
-Rescue Mechanics (WHY DID FE11/12 NOT ADD THIS IN AT ALL!? True, FE13 didn't have this, but it had Pair Up instead so I view that as a lateral extension)
-Conventional item trading. FE1/3 might have had this, I don't know, but FE4 did not.
-Weapon Ranks based upon usage of said weapon
FE3 had a speed threshold of 3 to double, which sounds workable in theory with a 20 cap for everything. I'm 99% sure 1 and 3 both had conventional item trading, but I can't be bothered to download either to verify this, especially now that 11/12 exist.
Gaiden chapters with specific unlocking prequisites is another major series element that FE5 pioneered, unless you count FE3 part 2's frue final sequence. Fog of War and Escape missions are two other things that FE5 came up with, though you might not consider those improvements to the series, especially FoW. <_< The 6-10 version of Fog that at least let you see terrain was a clear improvement over 5's implementation, though.
FE3 honestly sounds like it's the most polished of the three SNES Fire Emblems, which is kinda sad considering it was the first released. If 11 and 12 didn't exist I'd actually try it out since it sounds reasonably non-frustrating, but as it is I don't see much of a reason to bother unless I really want to stat cap Feena via FE3's hilariously broken growth-boosting shards/orbs and stat boosters.
Speaking of FE12, I've been sporadically playing a Marth+females+unarmed thieves playthrough through the past few weeks on Hard/Casual, just beat chapter 10 today. I'm definately glad I picked Hard instead of Normal now, because the extra enemy deployments genuinely make things more interesting. Take
C10 for example; since your fliers aren't forced to dismount like in FE3, they can easily move up and kill those two Bishops with siege tomes near the start of the map. On Normal, that pretty much reduces the rest of the map to just mop up duty, but on Hard and above they add a Sniper and 2 Mages with Shaver who can easily kill your fliers if you're careless. On the other hand, if you use Javs to kill the Bishops, you can safely stay out of the Sniper's range and only be exposed to one Shaver mage per Peg Knight, which is survivable. Alternatively, I've seen strategies for the stage that involve mass Snipers+Dracoknights clearing out pretty much every enemy in the central corridor on turn 1 with careful planning, even on Lunatic. Multiple strategies to handle a situation is cool, keeps the game from getting too puzzle-like (which is really bad in a game with randomized level-ups).
The drawback with FE12 and why I haven't played that much is that some of the maps ripped straight from FE3 end up being dumb and tedious. Like
chapter 3, which requires you to take a long circular path with low enemy density if you want to actually recruit all the PCs. Or
chapter 9, which was actually made worse than FE3 by adding an enemy whom only Marth can recruit to the left side of the map, one who starts moving if you enter the range of any enemy on the map, even the Dracoknights with huge move. I didn't want to burn a staff Rescue charge on the stage, so Marth needed dozens of turns just to recruit Etzel -> cross the desert to recruit Minerva -> cross the desert AGAIN to sieze the throne, one of the stupidest sequences in FE history. I don't really miss the Rescue command for any sort of combat purpose, but FE12 would be a much better game if you could have mounted units ferry Marth across the map, even if it didn't work on anyone else and completely killed the combat stats of the rescuer.