I am a graduate student in Sweden, and will present my PhD thesis next semester, and have several articles accepted/published.
However, when I applied (and got admitted) I had only studied at the university for three years, and only written a bachelors thesis. Me being admitted was sort of an "error" from the department, (and I had no idea what really was the requirements, since my thesis advisor encouraged me to apply).
Might this look bad on my resumé when applying for a post-doc position? (Or is young age an advantage, in my case, 25)?
I see no need for you to mention the lack of a masters unless asked.
I would definitely not say your acceptance into the PhD program was a error by the Department. This makes your university look incompetent, and you, at best, as uncertain and insecure about your accomplishments. You could also be perceived as dishonest by accepting admission if you knew it was a mistake, but I don't know the full details of what actually happened and why you believe this to be true.
You applied, you were accepted, you completed the degree, you are published. Full stop.
You seem to feel compelled to explain something that doesn't matter anymore, if it ever did. If asked, just say you were lucky and got accepted straight out of undergrad. If anything, it makes you look like a wunderkind.
An important caveat: All of the above is predicated on my understanding of the situation through the lens of a person with a PhD from the US.
As others have said, a masters is not always required for acceptance into a PhD program in the US, especially in the hard sciences (I know much less about liberal arts), but one is bestowed on the way to the PhD. So you get your masters after you are in the PhD program.