Women often ask how often Pap smear errors happen. They don't want to believe that there could be something wrong, and they prefer to wait a few months for a followup test. I can understand that.
I can understand that, because I felt like that, but remember that a Pap smear is not a diagnostic test. I mean that your doctor won't diagnose you with cancer from a Pap smear. It's actually a screening test--they use it to figure out who needs more testing. If you have an abnormal result, you need more testing, but what testing do you need? And when? Can it wait a while because everything else was normal (like negative HPV)?
Those are better questions than asking if there could be an error. Of course there could be an error! Humans look at your cervical sample, and humans can make mistakes. They can miss things. On the other hand, they can see things that look possibly abnormal that really are normal. What do you know about who reads Pap smears?
So, yes, there are false positives and false negatives on Pap smears. That's why doctors usually repeat it if they get a positive. There are other factors that play into the interpretation of your result. That's why a biopsy with colposcopy is recommended for some women after just one abnormal Pap smear, and some other women can wait for a repeat Pap test. What do you need next?