Well, the thing is that Lucas created quite a few issues between the OT and PT that were never dealt with until this series.
Padme dies and Leia was already taken away from her and yet she has memories of her mother. When Kenobi is around her in this series, she constantly reminds him if Padme. And there are several examples where Leia is obviously using the force to read minds and she could easily have seen Kenobi’s memories of her mother. She could also have seen some memories from bail as well.
Leia’s powers are subtle and are never manifested. Vader doesn’t sense her power. Kenobi doesn’t sense her power. Luke doesn’t sense her power. Yoda says there is another, another Skykwalker and Kenobi says it is her. So only Yoda picked up on it. Even the inquisitors didn’t pick up on it. So her power must also provide some cloaking. She isn’t a skilled pilot or mechanic like her brother and father. She is a skilled diplomat and politician like her mother. So no one notices she has great power and how it does manifest itself aids her in what she is good at.
Why would Kenobi make up the story about Vader betraying and murdering Anakin? Either he is hiding things from Luke, or now, he is using Vader’s own explanation. But there is no need to tell Luke where it came from. He tells Luke that certain things can be true from a certain point of view. Not just this. So he used it as a teaching moment.
And for the most part, this series is a few days where a few people call him Obi-wan again, but mostly they call him Ben. So he is exaggerating a bit when he says he hasn’t used that name since before Luke was born. Even the original dialog provides some leeway. And it isn’t like he stopped being called Obi-wan before Luke was actually born even without this series. The Jedi were destroyed before Luke was born and he is likely marking that as when he ceased being called obi-wan, even if that is not quite true per Ep III. This series doesn’t really change that. It just reveals a few people did call him that in a brief episodes.
One of the things about stories is that you have to apply a dose of reality to them. Taking every single quote as 100% fact does not reflect how most people talk. Most conversations have short cuts, incomplete statements, hyperbole, and don’t reflect the absolute truth. It is rare that someone can accurately relate the specific time since an event, like Sheldon Cooper, C-3PI, Mr. Spock, or Data constantly do. Most just throw out something that is roughly correct and writers write with that in mind. In fact writers are often more exact that real people ever are. Someone might throw out that something happened seven years ago in a conversation, but in reality it was 9 years ago. Times might be rounded up or down. And that is just the vagueness of time in conversations. Taking every word of dialog at face value is not a good way of checking realistic continuity (unless you have one of those very exact characters).
And Star Wars has always put the drama first. Things are not always described in great detail. The vagueness helps keep the hood on the magic behind the scenes. That is why Midichlorians were so objectionable - they opened the hood a bit and reduced the magic of the story telling.
So while there may be a few new quirks to the storyline because of this series, I think this series addressed most things well and answered more questions that it made. And any that it made are minor.