In Breaking Bad, Tyrus Kitt was stated to be a new hire for Gus' group who was assigned to monitor Walt after Victor's death. This made it seem like he was rather green to Gus' organisation.

This was changed in Better Call Saul, where it's revealed that he was working for Gus for years and was good friends with Victor. This changed the dynamic in the original show, where his frosty attitude towards Walt and Jesse is now due to his suspecting they had something to do with his death and blaming them for it.

Also in Breaking Bad, Saul's legal degree says he graduated from University of American Samoa in 1984, while in Better Call Saul, it's stated that Jimmy only became a lawyer relatively recently in the era where cellphones were already rather common. This would meant that the earlier degree is definitely fake... helped by the fact that you need to be a legal resident of American Samoa in order to be admitted to that university.