Is this a mistake in Harry Potter and the Half Blood Prince (the book)?

no this is not a mistake

if you recall snape's family was not very well off financially. Remember when he was younger he always had that oversized ridiculous looking frock coat. Also, in the memory that he gave harry in the Deathly Hallows, harry compares James' look of being well cared for with Snapes air of neglect and remember Snape's greying underpants when james hung him upside down by the lake. One would be safe to presume that Snape got his potions book second hand meaning that the book may very well have been published 50 years ago. Harry assumed that the book did not belong to his father or sirius who were both from wealthy families or any of their friends for that matter since they would not have gotten their books secondhand. Also, one would also be safe to presume that Hogwarts used the very same potions book 50 years later when harry was taking the class. the same could be said for the book: A History of Magic written by Bathilda Bagshot. By the time harry is in school, Bathilda is very old and she's "gone gaga" which means that the book was written a very long time ago even though it is still being used at hogwarts. Remember how the terrible night when harry's parents died and he survived is not even written in the book A History of Magic, so clearly it was published several decades ago, and the same is likely to be true for the Potions book.

No its not an error. It just means that the book was published 50 years ago and they still used the same books in James and Snapes' time.

Well that just means the book itself was published 50 years ago. Not that Snape used it 50 years ago.

It could have been around well before Snape used it.

This is the only explanation I can think of. Though I may be wrong, but whatever.

Happy New Years :)

This isn't an error; it was infact printed 50 years ago, but Snape got it later. Once Snape had it, we wrote all over it, declaring himself the Half Blood Prince.

Maybe the book was published 50 years ago, but Snape didn't get it till much later. Or it could have been his mother's book.

Just because the book was published 50 years ago, doesn't mean that they still weren't using the book to teach.

Not it's not because Harry was using spells out of that book (or tried) on snaps after dumbledors death and he was simply saying basically 'are you really going to use my own spells that I created/wrote down in the book. On myself the half blood prince' because until then Harry was t completely sure who the half blood prince was

Yes I noticed that. I think it was voldermort's book because he is half blood too. Then snape received or found it and he wrote in some of the things in it.

Maybe the book was published fifty years ago, but he didn't get it until he got to school.

Good observation. I would've never caught that :)

Wow....never noticed that...maybe Snape bought it second hand? :D