Bungie has always been very sketchy in regards to "Linking" the next game in their series. Halo 1 left you with the distinct impression that everybody, save Chief and Cortana, were quite dead. They even start you out in the first game with an abrupt "Arrival" to Halo. Absolutely no backstory given at all, save for a passing reference to Reach.
I presume they simply wanted the players to read the first book (Fall of Reach) by Eric Nylund. All of the Halo books are quite good, I will add. Fun reads.
Yet in Halo 2 you're right there on earth with Johnson. How you got there on a longsword (with no slipspace drive or real sort of navigation) is unknown. Even more, how Johnson survived is also a mystery.
Awhile later they make a book which explains most of this. Though Johnson surviving the Flood is still not really gone into detail other than an alleged Boran's syndrome which may or may not be ONI lies. Even so in the "Halo 2 Graphic Novel" there is a comic featuring johnson where he escapes from the Flood. This is considered Canon.
Halo 2 to Halo 3 is even weirder. Bungie "Implies" alot of stuff... They leave key details out of the spotlight and you just have to assume things (Which is annoying imo). For example the Forerunner ship (Dreadnaught) powering High Charity that Chief steals*, is actually the "Keyship" which must be used to activate the Ark (You see it in place over the Ark in H3). This was not really elaborated on, in fact many people I know just assumed the ship was part of the Ark structure and any similarity was just common Forerunner design.
Chief combating the covenant forces on the dreadnaught and being interrogated notwithstanding, Johnson, The Arbiter (Vadam) and Guilty Spark all arrive before he does. This is odd given that at the end of Halo 2 it's implied that the chief had arrived at earth roughly the same time the Arbiter dispatched Tartarus on Delta Halo.
There are also other continuity errors due to frequent retconning. The Brutes for example, which were unknown (allegedly) until "First Strike" the novel, made an appearance in Contact Harvest and Halo Wars. Johnson fought them, and even ran his Warthog into the old (supreme) Brute Chieftain.
They were also supposed to hold a diplomatic meeting in the gardens of Harvest.
The 19th Arbiter also shows up in Halo Wars as an antagonist, along with The Prophet of Regret- though whether or not his existence was known by the humans onboard the Spirit of Fire or others is unknown (Regret's existence, I mean). As the Chief and the other Spartan II's were ordered to capture a "Prophet" 20 years later by using the Pillar of Autumn to hijack a covenant vessel. This also implies that information regarding the prophets were sketchy, and that one had never been seen before.
This one I'm sketchy on: ONI had documentation regarding the "Existence" of an "Elite class" within the Covenant hierarchy that were expert combatants. This is implying that up until the Chief's direct confrontation with one onboard the station orbiting Reach, few had ever been seen in skirmishes. At the very least (and strangely) the Chief himself, a warrior who had seen countless battles with the alien menace, had not encountered one.
Yet they're plastered everywhere in the cut scenes of Halo Wars and in the game itself. Sgt Forge references the Arbiter as a "Massive Elite"- this game taking place roughly 20 years before the Chief had his first go at one onboard the station.
Totally bizarre.
Oh. And of course the Spirit of Fire combat the flood on the Shield World. So the Chief and the POA's Marines were not the first humans (outside of their forerunner ancestors) to combat the Flood in Halo 1, apparently.
*How High Charity was able to sustain slipspace jump without the Dreadnaught's reactor powering it and crashing into the ark is also, a total mystery. (10% of the reactor was used to power all of High Charity). Unless Gravemind and the flood have mad power generator building skills....