A whole lotta stuff:
1) The opening sequence. Way to promote negligent and unsafe parenting by having your kid ride in the back of a moving truck, where any hard braking, cornering, or large bumps could send your kid tumbling into a wall of the truck, a packed box, or any number of pieces of furniture, or have any one of these unsecured articles fall on top of them. Boom - your character's dead before even starting their journey, with a massive bloody mess in the back of the truck. If I was placed in R/S/E's scenario, I wouldn't even concern myself with training - I'd be contacting Child Protective Services and my attorney to sue the pants off Norman and whatever the mother in these games is named. If I even lived through the ordeal, that is...
2) Excessive water! In particular, the water routes between Pacifidlog and Slateport with the currents that you had to traverse multiple times just to collect everything and battle everyone. Way to artificially extend the gameplay in the absolute WORST way possible. The very definition of pointless tedium.
3) Match call system where trainers forced you to take their number without giving you the option to refuse. Seriously, at least the Johto games gave us the option to say "No" when asked if you wanted to exchange numbers with an NPC.
4) Gym Leaders with only 2-3 Pokemon, and Elite Four members with only four Pokemon.
5) Wallace as Champion. Steven was tougher to defeat AND with Steven at the helm, you didn't have two Water-type specialists in the late game (Juan 8th gym leader and Wallace as champion shortly thereafter).
6) World tournament. Emerald's Battle Frontier was much better.
7) Random cameo appearances from other games. It's almost never pulled off without seeming needlessly tacked on (see prior point)
8) One specific, highly overrated character from a previous game in particular. Those who know me know exactly who I'm talking about, and I'm not going to elaborate further on that point.
9) Two bike system. Why force us to return to the bike shop repeatedly throughout the game?
10) The idiot on the cycling road who says "Rydel" repeatedly and wastes precious time.
11) The clunky fishing system that was made needlessly complicated.
12) A rival who gives up after gym #6. Seriously you had one "rival" who battled for 2/3 of the game then gave up, then a kid you only met twice (and fought only once) takes up that vacated position. Perhaps I should add, "boring, passive rival" to this as well.
13) The "Bait, Rock, Ball" Safari Zone system. I never liked that in ANY game.
14) Getting rid of customizations. If I have to stick with May's default look I will officially be crossing these games off my "to buy" list. Right now they're on the "maybe" list because of many of the other things I've mentioned.
15) I'd like to say "Hoenn" because that was my least favorite region, but I realize that's gonna be impossible lol
16) "Pika Pika!" Seriously, hearing that annoyed the hell out of me in X/Y.
17) Dive. I know it's critical to R/S/E's storyline but (a) dealing with yet another Water HM on top of Surf AND Waterfall is just annoying, and (b) it doesn't make logical sense how your character can go underwater, with no scuba gear, and not suffocate to death.