From alexwlchan's excellent answer here (emphasis mine):
I know that Harry Potter Wikia isn’t usually considered canon, but they have a list of dating contradictions which looks fairly accurate. To me, most of this list can be written off as JK Rowling's dodgy maths, but I thought I'd pick on one example.
For example, in Goblet of Fire, we have Friday the 30th of October and Tuesday the 22nd of November. If you look at a calendar, you see that 22 Nov falls 23 days after 30 Oct, so the 22nd is a Sunday in the Gregorian calendar. There are many possibilities:
- Whoops, JK Rowling messed up.
- Their weekdays occur in a different order to ours.
- The magical calendar puts extra days at the end of October.
- There are some "glue" days between months to make up the difference.
- Unclear as to whether to start months from the 0th or the 1st day, they compromised and count November from the (-1)st.
- At some point, several days were dropped,1 but nobody thought this was remarkable or unusual.
I think the only plausible explanation is (1).
More details from that HP Wikia page on dating contradictions (emphasis mine):
Often when dates are given, they are given with a day of the week that does not match with that date as it in actual history. One such example occurs in Harry Potter and the Prisoner of Azkaban when Sybill Trelawney refers to 16 October as Friday, although 16 October 1993 was a Saturday. This is usually explained as artistic licence on the author's part.
There are also contradictions within the books in this area. For example, in Harry Potter and the Goblet of Fire, both 1 September and 2 September are given as Mondays and, in Harry Potter and the Prisoner of Azkaban, Buckbeak's trial is set on 20 April, but careful parsing of the text reveals that it could have happened no later than February.
Also, if an anachronism counts as a dating error, then we have How could Dudley have wrecked his PlayStation if the PlayStation didn't exist yet?:
Harry was born in 1980. Therefore, the fourth book should be set in 1994. Yet, Harry mentions in his letter to Sirius that Dudley chucked his new PlayStation out of the window. The only problem is that the PlayStation wasn't on the market in Britain at that time.
From Slytherincess's excellent answer here:
I think we have to take the number of students at Hogwarts with a grain of salt. J.K. Rowling has discrepancies in her numbers, and she admits she is "horrible at maths," but at one point it was put forth that there are approximately 1000 students at Hogwarts, which would break down to approximately 250 students per house. There's a short article on how many students there are at Hogwarts here. The number of students in each house does indeed seem evenly distributed.
However, the answers to During the events of the Harry Potter series what is the total population of Wizards/Witches globally? contradict both this and each other. In particular, one of them mentions two very clearly contradictory statements from JKR:
Also, J. K. Rowling has stated that she imagines the wizarding population of the U.K. to be around 3,000. This estimate, although seemingly small, is understandable; a larger population would be far harder to hide from Muggles. However, she also stated that the number of students attending Hogwarts was around 1,000, which seems inconsistent with the population estimate.
Here are the words of JKR herself in the famous "Oh, Emerson, my maths is so bad" interview:
I sat down and I created 40 kids who enter Harry's year. [...] I never consciously thought, “That's it, that' s all the people in his year,” but that's kind of how it's worked out. Then I've been asked a few times how many people and because numbers are not my strong point, one part of my brain knew 40, and another part of my brain said, “Oh, about 600 sounds right.” Then people started working it out and saying, "Where are the other kids sleeping?" [...] But if you assume that all of the wizarding children are being sent to Hogwarts, then that's very few wizard-to-Muggle population, isn’t it? There will be the odd kid whose parents don't want them to go to Hogwarts, but 600 out of the whole of Britain is tiny.
Let's say three thousand [in Britain], actually, thinking about it, and then think of all the magical creatures, some of which appear human. [...] That's going to bump you up a bit as well, so it's a more sizable, total magical community that needs hiding, concealing, but don't hold me to these figures, because that's not how I think.
The problems with, and contradictions between, these figures have been much more extensively discussed in Shisa's excellent answer to Why is the intake of students for Hogwarts so small compared to the number of witches and wizards in Britain?. (As an amusing side-note, after the above-quoted paragraphs, the subject was quickly changed to lovey-dovey stuff, on which JKR was much happier to expound.)
- How could Hermione have gotten more OWLs than classes? Apparently JKR originally wrote Hermione as having taken twelve OWLs, even though she was only taking ten classes from her fourth year onwards.
- What age did Dumbledore live to? Slytherincess's answer here highlights contradictions between different JKR statements on Dumbledore's age.
- Why doesn't Hogwarts have more teachers? The number of teachers and students at Hogwarts doesn't really work out to give every teacher a realistic workload. (Admittedly JKR is far from alone among authors of kids' school novels in making this sort of story-simplifying 'error'.)
- The Weasleys' ages. (This link was actually mentioned by alexwlchan in the first answer quoted above, but I thought it was worth including as its own example.) JKR once messed up the numbers for the age difference between the Weasley boys, specifically Charlie and Percy.
Hat tip to DVK on meta and Valorum in a comment and alexwlchan in an answer for pointing me in the direction of some of these maths errors.