Why is Gintama's episode 305 full of contradictions? So episode 305 came out recently, therefore spoiler alert.

Most of it is concerning the past...

In the past episodes' flashback it was shown clearly that ..


in this video,Takasugi lost his eye in a fight with alien. 
Shuoyou, teacher, is taken from his school and then his is returned to gintoki who cries helplessly.
Shuoyou finds gintoki on battlefield and bring him to class with katsura and takasugi in it.


However in episode 304-305, this all contradicts 


Takasugi loses eye by attack of Oboro
Katsura, Gintoki, and Takasugi are brought as prisoners and Gintoki is given choice to kill either students or teacher, on a top of mountain. Contradictory, to what been shown before many times: which is soldier hold gintoki down as teacher is taken prisioner and then on the same place his head returned and gintoki cries.
In this version, gintoki is already part of the Shuoyou school and it's infact katsura and takasugi who join later on.
Much like @Akaik mentioned in his answer, the main reason for the inconsistencies is entirely down to both Sunrise and Gori-Sensei not entirely knowing the details of these events as they go head first into making everything.

They pretty much admit to this using Gintoki to explain at the end of episode 306, where they include another Ginpachi-Sensei segment.  They even use the point you mention that previously it looked as if Gin joined Shuoyou's school after Katsura and Takasugi, when in the latest episodes it appears to be the reverse.  They make a joke about it not having a script at the time and that something entirely different is happening.  

This is probably as close to an offcial answer that we'll get.

There may be other mentions to why the other points you make out have changed in-between episodes but no mention of this (even as a joke) has appeared in the manga as far as I remember.