I just watch ep.8 season 1 I Robot, You Jane. When Malcomb first see Buffy he looks up her school records. It list Buffy Birth encontro, data as 10-24-80. However when Frits looks at the same page the birth encontro, data for Buffy is 07-26-79. Error or what?

The short answer? Yes.

The best explanation I can think of is that season one was still their first season, and they were working out all their kinks and bugs and didn't have set plan or character details yet.

Buffy's actual birthday was determined cannonically probably in season two, when they celebrated her birthday for the first time in the series on January 19th in the episode "Surprise." As that's when the episode aired (in 1998), January 19th was decided to be her birthday. I'm not sure if that's what the writers decided, or what the fãs assumed, but after "Surprise," Buffy's birthday episodes always aired on or around January 19th.

It was also decided, since she turned seventeen on on January 19th, 1998, simple math determines that she was actually born in 1981, which are neither of the dates listed in the episode "I Robot, You Jane."

Ergo, I can only assume that the discrepancy was writer error, as they probably had not decided among themselves when Buffy's birthday would be.

PS: Excellent catch, though. I never noticed that before!