Despite Rick Riordan's best intentions, there are mistakes in the Kane Chronicles series, either based on continuity, mythology mistakes, or character flaws. While some of these have explanations, even coming from Rick Riordan himself on his blog or Twitter, not all are explained directly in the books and can still be considered mistakes. There are also other errors in the series that may never be explained and can only be considered mistakes.
The Red Pyramid
In the Red Pyramid the moon god is called Khons but in all the other books he's called Khonsu.
It wasn't Nut who gambled with Khonsu, but Thoth himself who did the gambling, as he was able to offer secret knowledge if Khonsu won.
Anubis was actually the son of Osiris and Nephthys as a result of Nephthys either disguising as Isis or getting Osiris drunk.
This was likely an intentional change made to try and make the books more kid-friendly.
Egyptian myths, like Greek myths, have many different versions. Some stories do say that Anubis is the son of Nephthys and Set, while others say he is the son of Osiris and Nephthys. It is possible that Riordan chose the more kid-friendly version.
The Throne of Fire
When Carter, Sadie, and Bes are discussing where Zia used to live, they translate the Egyptian village known as Al-Hamrah Makan (meaning The Place of Red Sands) word-by-word. As doing so, they reverse the meanings of the words. Al-Hamrah means red, and Makan means place, not the other way around.
However, some languages require the meaning of the words to be reversed in translation to make sense, so it is possible that Al-Hamrah Makan is how the natives would say The Place of Red Sands and that the translation is not acutally intended to be word for word.
While describing Walt,Carter says "Walt was the same age as me, fourteen".But while talking to Sadie in the desert, Walt says he is sixteen.
The Serpent's Shadow
It is extremely odd that Setne was portrayed as a villain in the book, as in classic mythology and history he was considered a hero, and even returned The Book of Thoth after realizing what the consequences of the theft would be.
On top of this, Setne did not steal the book from Thoth himself, but from the grave of another man who stole the book. It was this man who threatened to curse Setne if he did not return the book to his grave. Thoth himself only had the first thief punished. See here for the full myth
As Carter Kane had absolute authority over Bloodstained Blade, he should have been able to command Bloodstained Blade to stop trying to kill him, and tell him to no longer take any orders from Setne. Bloodstained Blade is bound to the Kanes, and thus Carter's commands should have overruled Setne's commands.
The Sadie in the artwork and the Sadie in the books do not match. One of the most important characteristics, the stripes in her hair, was not featured in the image.
It is well known that the official illustration of Thoth does not match his description in the books either for the following reasons:
Thoth's hair is described multiple times as golden blonde, while his image shows him with brown hair.
In the books, his lab coat is covered in writing, while in the official image, it is clean.
He appears to have stubble in the official image, while in the books, no stubble is mentioned.
The Kane Chronicles Survival Guide
In the section on Hieroglyphics, a guide is given to help the reader translate a page that would reveal Set's secret name. However, the books themselves point out that knowing the words of one's secret name is not enough to actually learn it, as one must learn a secret name from someone who is close to that person in order for it to have power. It even specifically says you cannot learn it from a book. Thus, providing Set's secret name in the guide would be next to useless as learning it from the book would not give the reader any power over Set.
In the illustrations, switchblade demons are not portrayed as having switchblades for heads, as described in the novels, but rather regular looking heads with blades on them.
In the section on portals, a picture is shown of what the caption says is the portal at Baharyria. However, that place is specifically stated in the Throne of Fire to have no portals, necessitating the use of the portal at Alexandria.
The Demon Days are the last five days of the year, so in the books they are December 27th, 28th, 29th, 30th, and 31st. However, the Ancient Egyptians used a different calendar than the one we use today (the Gregorian Calendar) that ended in mid-July.