One dealt with the last names of most of the X series characters (Signas Lancaster, Marty Gisbon, Iris Thorne, etc.). The best was "Zero Omega."
Zero killing most/the whole cast of the original series (this has been Jossed). This was popularized by Bob and George.
The DWN Robot Masters living in Wily's fortress in-between/during the games. Probably canon for the TV series, but that's not the same continuity.
Speaking of Robot Masters, fan works are more susceptible to the idea of female Robot Masters (or Robot Mistresses, if you will), who are barely seen in-universe. (The only canonical RMs of that nature are Light bots Roll and Splash Woman, plus Plum from the Battle & Chase spin-off racer.) This actually seeped into other, non-official continuities, as the manga for Mega Man 6 had its incarnation of Centaur Man revealed to be a woman with long, flowing hair and the Archie comic introduced Tempo/Quake Woman, an OC creation of a former colleague of Light's named Dr. Lalinde, as well as her sister Vesper Woman (who is based, in-universe and out, on Honey Woman, the original design for Hornet Man).
One of the biggest problems is that early Mega Man (not Rockman) stuff was prone to embellishment, so much that it could be considered its own continuity. That in itself isn't too bad—this happened a lot in the NES era—but many fans aren't too happy with it. If they don't dismiss it all as mistranslations, they claim it's compatible with the original canon material, despite not perfectly overlapping at all, and then embellish further in order to explain certain points or cover plot hole (absolutely not helped by some people considering fan translations of dubious quality or fanfiction as canon, nor by assuming that everything the Japanese fans said was true; that's where those last names came from). While it's not as bad today as it was in the early days of the community, there's still people who think/insist that Doctor Light and Wily being partners is true for all regions, or that Mega Man knows that Proto Man is his brother in the Japanese continuity.
In the Battle Network series, the premise of MegaMan.EXE and Lan Hikari's link has been debated in fanfiction due to its vagueness of detail in the games. Many fan works will include the link as having the two be able to communicate telepathically or control each other's bodies.
According to fans, Mega Man Zero occurs in 22XX, a century after the events of Mega Man X. (By proxy, this places Mega Man ZX circa 24XX.) Though taken to be true by many, this claim is actually a slight corruption of canon, where Zero takes place a century after the Elf Wars, an event that in turn follows the X series, which have been Left Hanging with X8. (Word of God also states that Zero's ending from X6 is the last event in that series' timeline.) The Zero games themselves never offer an exact chronological reference point, and while non-canon, Command Mission itself takes place in 22XX, with no signs present in-game of a bloody conflict initiated by a madman with a god complex that almost claimed all sentient life on Earth.