The limitless bag would work better if they made more pockets. Of course, if they did then we'd all be complaining about too many pockets make for slower item accessibility. Perhaps sub-pockets accessible through the main ones would work better?
Personally, I like the bag because I've always hated storing items on the PC. Things that bother me include the following (and possibly others I didn't think of at the time of writing):
1. The less-than-originality of the town names. Come on, Sandgem Town? Hearthome City? Twinleaf? Snowpoint? Sunyshore? I hate the random compound words for names; this goes for the 3rd gen. as well. I liked it much better when they were colors or plants. If compound words is the new thing, then they shouldn't make the combined words that obvious (Mauville and Canalave were alright.)
2. I don't like the way that the number of pokemon displayed when saving is the number of pokemon seen, not caught. I always put a higher value on the caught number; "seeing" them all is rather unimpressive to me.
3. Really, really, really, really, really slow Surfing. Seriously, why can't surfing be at running speed? I never liked sea routes, but now I hate them even more.
4. Making Poffins. It's a chore; at least with Pokeblocks you could do it fairly quickly and I liked the timing game involved. Stirring and then randomly having to stir in the opposite direction is just a pain. Plus, I hate the overflowing.
5. Surf. Again. Was it really necessary to make it hit your own teammate? Surf was bad enough in double battles as it was. The only way I can see it being useful is if your ally has Water Absorb (and I've never trained a pokemon other than Vaporeon that does)
That's all for now; I'm sure I'll think of a few others later.