...that in some of the pages the achievements repeat?

For example Page 3 under Pets It starts with Quitter but further down the Quitter achievement is there again. As well as Rare Toy, SAI Worker, Six Pack, Souped Up!, and many more on this page and others.

Is this a mistake in the coding or something else?

i could be 100% wrong, but my guess is that when you go to the next page it just lays over the previous page, so if the page you're on isn't completely full, it shows some achievements from the previous page (almost like the page is peeking through). That's just the pattern I've noticed.

This is a known bug. Mostly I've noticed that it tends to happen randomly. As far as I know, other than being confusing, it doesn't affect anything. Achievements are still triggered/awarded/counted, etc.

This is happening to me on all achievement pages except page 1. So if there are 4 pages in one achievement category my achievements get repeated on page 2, 3 and 4.

It must be an error in the coding, but there are more important things like the new wardrobe right now :)

Yeah, I have this error on pretty much every page... Each page shows every achievement twice. It's really annoying, but doesn't prevent me from doing anything, so I guess it doesn't matter so much. Sometimes I get really frustrated in the Subeautique ones, though... If you click to show the necessary items, but you're looking at the second version, it will look like nothing happened, because the items open up in the first version, not the second where you are. :O I think I tried to open some of them ten times before I figured out why it wasn't working.. :O