Naturally, the GTS serves as a feature that does the complete opposite for those wishing to complete their Pokedex, allowing access to only the Pokemon they have seen. But with that, some of the requests on there are truly ridiculous, such as a Level 3 Bidoof requesting something like Dialga or Giratina.
Second would be the honey trees. Having to wait for Pokemon to be lured... okay, its a nice thought, but the fact that it takes so long for them to appear and you only have a slim chance of finding the rarer Pokemon that are attracted by honey, it all becomes a truly ridiculous feature.
Third would be the Game Corner in the European version of Platinum. It was probably the stupidest thing Nintendo and PEGI could have restricted. The reasoning behind it; encouragement of gambling, is about as idiotic as a rating system can get, because the game was far from being something encouraging gambling. You could just buy the coins, for crying out loud! I occasionally liked to play around in the slots when I had nothing to do, but I'll have to have that option open to me by continually importing my games...
For all it's logical worth(lessness), I'm surprised they haven't told Nintendo they can't make Pokemon a 3+ game any more because it has Pokemon fighting in it and thus contains depictions of violence, or promotes criminal acts by pinning a 10 year old against a fully (dis)functioning criminal organisation, stealing peoples' Pokemon, etc. Heck, even discrimination if we really want to stretch the elastic that far. (just as small as the Game Corner, the first Gym Leader says something like, "I can't believe I lost to a trainer with no badges..." which, stretching the boundaries of discrimination to their absolute ridiculous limit, could be seen as such, I suppose. In their eyes, anyway, I'm sure)
I guess my final one would be the lack of Fire-types, though generally in relation to the lack of them throughout the Pokemon Generations. It can't be that hard to think of new Fire-type Pokemon to give more variety. Heck, Water-types had roughly double the number of Fire-types in Generation I, I believe and though I have not counted, must be triple, by now. Though in particular, to make this Diamond/Pearl-based, the use of Fire-types as an Elite Four type. As noted, only two of his Pokemon are actually of the Fire-type in Diamond and Pearl. I mean... he even had a Steelix in his team. That's right, a Steelix. What the hell!?