Let's remember that retcons are not necessarily logical impossibilities. Goku and Piccolo being aliens instead of a human and a demon, respectively, is still a plausible idea. Now, maybe it was not obvious enough during the early days of Dragon Ball, but there were always hints that most of the main characters were not normal creatures. Super strength and science-defying abilities tend to give the impression to the audience that normal human beings can't do that.
Going back to my earlier comment about retcons not necessarily being impossibilities, suppose that Bulma, being the scientist she is, took a blood test on Goku and it was revealed that he has human DNA, but years later Raditz arrived and told Goku that he was actually an alien. Unless we get some explanation that the test was faulty, the notion that Goku is an alien wouldn't be a retcon; it would a plot-hole.
Anyway, most people here have already mentioned the big ones (Goku is not human, New Dragon Ball Rules, etc.) but here are some that, while perhaps not being the biggest, have caught my attention more so than usual every time I examine the franchise.
1) The Pilaf Gang still existing
. I'm not just saying this because I have a nuclear-powered hatred of them, but even though we see them survive their fall from the sky and find out that they were apparently turned into infants, who the HECK took care of them!? Not only that, but before the whole Battle of Gods storyline fiasco was ever introduced, I always found it so surprising that they were considered good enough to be brought back to life and be part of DBGT.
2) The entire Majin Buu Saga.
We all know that Toriyama never plans ahead, but it just seems that while previous arcs have some connection with each other either through foreshadowing or as an effect from a cause, the whole arc feels so disconnected from the progression of the story. I still like it, but it would have been better if they could have at least tried to explain plausibly how Majin Buu appeared earlier in the Main Timeline than in the Original Timeline and the others. Had it not been for the Future Trunks arc and the episode/manga where we see Future Dabura and Future Babidi, you would have assumed that Majin Buu just never existed in his timeline! My own head canon states that the fight with Cell attracted the attention of Babidi as he was traveling to space. *shrugs*
3) Previously unknown siblings such as Tights and Tarble
. ...yeah, those are self-explanatory. I'll also add that while I have never read Jaco the Galactic Patrolman, I don't like the idea of it being a prequel to the Dragon Ball manga and its inclusion of Jaco trying to hunt down Goku as a baby. :/
4) The ever-increasing levels of deities (aka, Kaios and Kaioshins, Hakaishins, Makaioshins(?), etc.).
Not as complicated as most retcons, but I find it annoying every time we are told or given the implication that NO, THESE GUYS ARE THE REAL GODS THAT ARE SUPREME, FOR REAL! At least we finally have the Omni-King, though. Unless...