1. Surfing Speed. It makes Surfing in the first and second generations look like you're riding a jet-ski. As for the third generation, you may as well be flying an airplane when you compare it to surfing in the fourth generation. I loved the surfing speed in the third generation; I was pretty appalled by the sluggishness of surfing in the fourth generation.
2. Saving a lot of data. I get this message a lot, even if I've only been playing for about five minutes since the last save. What major thing could I have done in the last five minutes that made the game take so long to save?
3. Secret Bases. I liked being able to build a Secret Base in a tree, cave wall or bush, back in the third generation. The interiors of the rooms all seemed to have a unique shape. In this generation, it's pretty boring having to build your base underground.
Plus, I can't get rid of the rocks in my base. Apparently, I need to connect with someone over Wi-Fi to do it, which I don't see happening anytime soon. I don't have access to a Wi-Fi connector or a wireless connection, and no one I know owns Diamond or Pearl - so I'm stuck with the rocks. Great.
4. Having to tote around a ton of HM-using Pokemon. I have three HM slaves - Starly, Geodude and Budew - and I hate having to drag these guys around on long expeditions (i.e. the trip up to Mt. Coronet's peak). It means I have to deposit one or more of my good team members in the PC to make room for my HM slave(s). It seems there are HM-requiring obstacles everywhere you go.
5. I'm one of those people that dislikes the absence of a "back" button on the Pokétch. It's annoying having to flip through a while pile of useless aps to get back to the digital clock.
6. I actually wasn't aware until recently that the item bag had infinite space. However, I was getting suspicious of something like this being true, having made it through seven gyms, collecting a ton of items, and not getting the "no more room for items" message once. That said, it's irritating having to scroll down for ten minutes to get to the item I want.
I actually didn't find the whole "battle with Palkia" thing annoying. The game lets you save right after beating Cyrus, provided you don't immediately march on ahead to face Palkia/Dialga. As long as you've packed plenty of healing items and Ultra Balls (or whatever kind of Poke Ball you prefer using), you should be all right to face the legendary Pokemon.