My thoughts on the matter, just to be clear:
I really appreciate Wi-Fi trading and the like, and I personally think that we were much worse off when the only way to find someone to trade your Kadabra with to evolve it was to actually find someone to trade your Kadabra with to evolve it. That said, they haven't made very good use of Wi-Fi yet. Only recently have they begun to hold Wi-Fi events for event-only 'mons, and unless something has changed since Platinum, the GTS still only allows you to seek Pokemon you've already seen, which rather defeats the point of the GTS. I mean, correct me if I'm wrong, but most of the 'mons one has already seen can be expected to have already been caught. Not all, but most. You also can't customize your search parameters nearly enough for my taste. You can set what level and gender you want the Pokemon to be, but that's about it, if I recall. So the big problem at this point is the lack of options.
Or, at least, the big problem with multiplayer functions.
The other glaring problems with the series have already been discussed at length.