Let's see. It seems to me that the 2001-2003 story was mostly tied up, I can't think of any real loose ends. Maybe the Makoki stones...
In 2004-2005, the biggest loose end was probably Krakua's appearance in Time Trap; Greg told us that Krakua had established the communication with Vakama while protecting a fortress in the future, but that episode was never shown and we were left wondering exactly how the connection established itself, why Krakua talked about those particular things with Vakama and so on.
I also think the past of the Rahaga might have been explained better: while the main elements (raid on a Brotherhood fortress, theft of the Avohkii, transformation of four Toa into Rahaga, rescue...) were there, the exact order wasn't clear (apparently there was a battle with Makuta Teridax, but when exactly did it occur?) and even later answers by Greg failed to fully dispel the ambiguity.
In 2006 Jaller & co. became the Toa Inika by being blasted by lightning from the Red Star. That transformation was never explained until after the end of Bionicle, when we were given a lame retcon saying it was yet another failsafe system built by the Great Beings.
I would also have liked to see tied up some of the stories about the Dark Hunters that appeared in the Dark Hunter guide. Too many were described as being on missions whose conclusion we never saw, forcing Greg to later basically say that all of them had failed; I think at least the Dark Hunters tasked with capturing the Piraka could have been given some closure.
In 2007, the largest gap is called BIONICLE Legends #7: Invasion, the book about the descent of the Toa Inika down the Cord that was never published, which should have featured Makuta taking over Matoro, Vezon attacking the Toa Inika and being captured by the Zyglak and so on. All these things were canon, but they were only mentioned in guides, which was a pity.
That was also the year serials began, which gave us some additional stories but also a great deal of inconsistencies (how did Karzahni get to the Pit with his entire Manas army? How did the Toa Nuva know where Odina was and how did they travel throughout the universe?...)
2008 was a messy year, where we never fully understood the order of the serials. If I were to name gaps, I'd say the draining of Takanuva's light (we later learned that it was Icarax who dropped the shadow leech to drain Ahkmou's light... but there are a lot of unclear issues with this explanation, such as why Icarax of all people went after a Po-Matoran), the Mask of Time (disappeared when Voporak took it, we never learned what became of it) and Brothers in Arms (this wasn't strictly a gap, but there should have been a lot more about Vultraz's and Mazeka's conflict, instead of it all ending with a dimensional hop and an alternate universe).
2009 was the year where the major gaps and loose ends began. Baterra, Element Lords, the second journey of Tarduk, later joined by Mata Nui, to the Valley of the Maze (we only saw bits of it), the Sisters of the Skrall (their appearance in Sahmad's Tale was just a way to get rid of them), some characters that never or almost never appeared (Perditus), some issues about the Glatorian population (there were veteran Glatorian and nameless rookies, with people like Metus recruiting new ones... but from where?) and probably more I can't think of right now; plus all the open-ended plots of Reign of Shadows.
Don't even get me started with 2010 and the never-finished serials.
Some additional, recurring inconsistencies, in my opinion, where related to geography and knowledge. In the former case, Greg never managed to create a coherent geography of the MU: the structure of the domes and of the sea gates was never completely described and people just seemed to get from one place to another without any regard for distance or for the existence of a connection between two locations (Karzahni's journey to the Pit, Brutaka's team journey from Tren Krom's island to Artidax); the MU map also had major problems.
As for Bara Magna, the size of the desert and the time it took to cross it kept changing; there was also the issue of the giant robots' sizes (a 27 million feet tall robot as big as the village of Tesara...) in comparison with the desert's and the geography of the regions of Bara Magna and Spherus Magna that were not depicted on the official map.
As for knowledge, this is something of an obsession of mine. Basically things that were at some point a mystery (to name but a few: Nidhiki being a Toa; the origin of the Rahkshi, which was unknown to the Matoran of Metru Nui; Antidermis; the fact that the MU was contained in a giant robot) then suddenly became common knowledge. How was that possible? Greg's answers on this point never fully satisfied me.