Well in Diamond/Pearl/Platinum-
-The same pokemon for several routes. I understand Starly,Bidoof, Budew, and Shinx are supposed to be the "common creatures" but the first 4 or so routes has nothing but them, then every route after that for the most part has them or an evolved form of them. They are all fine pokemon and I have no other problem with any of them, but this bothered me. Also probably why everyone hates Bidoof. Thankfully Platinum toned it down a bit, but its still a problem for the first 4 routes, but that's at least in-line with other generations a bit more.
-Team Galactic being pushovers. Except for Mar's Purugly and then the battle with Cyrus at the end, Team Plasma where no real threat in Diamond and Pearl. The Grunts get level 40 Wurmples.. Platinum fixed this at least. Yes I know Team Rocket wasn't exactly a threat either, but they at least had more threatening things than the "starter bug". Same goes for Magma/Aqua if I remember right.
-Like everyone said the lack of fire types was a problem. Fixed in Platinum however.
-The introduction of Stealth Rock to the Metagame was aggravating. Black and White fixed that a bit at least.
-Not letting you buy revives before the 3rd gym. This is mainly a problem in Platinum. Fantina's Mismagius is the bane of my playthroughs in Platinum, the fact you can't buy Revives to at least try and stall her bothers me. The thing has way too high of a special attack for a 3rd gym pokemon and unless you use torterra or manage to raise something quick and strong enough to OHKO it or manage to survive its shadow ball you will be cursing at your DS.
-Amity park. Kind of a nitpicky thing, but I never saw the point of only letting cute things in. I know this was basically a way to test the "following pokemon" feature for HG/SS but "cuteness" is in the eye of the beholder. I for one happen to find Larvitar adorable.. grumble..
-Defog and Rock Climb. If you are going to force us to teach all these HMs at least make them halfway decent in combat like Surf is. Defog should clear away weather IMO.
-Elite four not having a team full of their chosen type. Fixed in Platinum, but still Don't pick a fire Elite four member if there are two full evolved fire types in your pregame dex... Volkner suffered from this too.
-Garchomp being cheap. Just a personal gripe.
Heart Gold and Soul Silver-
-no real problems I just wish Gyarados's following overworld sprite didn't look so...odd.
-EDIT, whoa I can't believe I forgot about the stupid Youngster who calls you every five second to tell you about his Ratatta..