So Ben said Charlotte was born in 1979.
In this episode it's apparently 1974 and little Charlotte looks to be 5 years old.
Now, I know Ben is a major liar, but what would be the point of him lying about something like that? It wouldn't accomplish anything for him... he has no reason to make a tiny unimportant fact like that up.
I think Ben had a few things wrong about Charlotte. He was spouting off facts as given to him by Michael. Charlotte and Mom obviously left the island pre-purge, so I'm guessing that there were some fake identities made for them to assimilate with the outer world - and to protect them. A different date of birth isn't a big deal.
I think we have to ask ourselves who is Ben getting his information from about those on the freighter?
We know he's getting the names from Michael, but only names. Who is Ben relaying that information too? I think whoever that person is, is controlling the flow of info to Ben.
Obviously if given accurate information on Charlotte, he would have known she was born on the island. Also, he would have known who Daniel Faraday's mother was. That seemed to come as a shock to him as well.
I don't think it's a mistake by the writers. I think whoever Ben's source is in gathering that intelligence, is misleading him on purpose. Mrs. Hawking perhaps? Goes to show that Ben can be fooled and is not all knowning.
ETA: Wow. You type a response and go to hit post in a blank thread and your five deep by time it pops up Nice.