First, the way trading was handled. In literally every other Fire Emblem game, you traded weapons by putting two of your units next to each other and selecting "trade". That's not the case in Genealogy. In Genealogy, you have to go to your castle (or any castle you've conquered), go to the Pawn Shop, sell the weapon you want to trade, then have the receiving unit visit the Pawn Shop and buy the weapon you just sold. Why? What was wrong with the original trading system. The way FE4 handles it is just long and unnecessary.
My second problem is that its nearly impossible to save the villages. Bandits spawn right next to or on the village. Yes, they take time to destroy but by the time you get there, it'll be too late. The only way i've ever been able to save those villages is by using an infinite turn cheat code.
My third problem is the redundant classes. You've got some cool classes like Axe Knight and Swordmaster, but then you've got ones like Lance Knight, which is just a Lance-locked Cavalier. I know why they did this though. They needed to justify having static weapon levels.
Problem 4 is the way marriages are handled. In terms of child characters, FE4 does it better than Awakening and Fates. In terms of how the characters actually get married, Awakening and Fates do it better. In Awakening and Fates, you see the characters interact and there's as sense of progression. In Genealogy, you won't know if two characters got married unless you check their status screen. For a game that introduced the marriage system in Fire Emblem, there sure is a lack of character interaction. The most you'll get regarding couples is that conversation that they have at the final chapter of each generation. There are other conversations too but those are very specific and are chapter dependent.
Problem 5 is that Great Shield activates too much.
Problem 6 is that enemy's can switch weapons during the player phase. Unless your fighting an enemy with one weapon, your always gonna take damage.
Problem 7 is that the minimum promotion level is lv.20. This is a personal thing though, because, due to my impatient personality, i always promote units ASAP. But i can't do that in Genealogy. Also, an odd thing is that levels don't reset upon promotion in Genealogy.
Problem 8 is that Corple is the worst unit in the series. As someone who loves training Est-types, seeing as how they end up being some of the best units in any FE game. But for Corple, being an Est-type is more of a curse than a blessing. Who thought it was a good idea to have a Staff-locked Est-type join two chapters before endgame in a game where the minimum promotion level is 20?
Problem 9 (and the most unpopular FE4 opinion of all) is that i find Sigurd to be incredibly boring, to the point where a block of wood is more interesting. The guy has no weaknesses, both personality wise and gameplay wise, making him an extremely unrealistic character. Like, if he had at least had a weakness gameplay wise, such as low growth rates, then i'd like him more. But he's just too perfect and i don't like him because of that.