In the credits for Batman Begins the baby is listed as James Gordon Jr. He's also mentioned in the Batman Begins novel. So the two films are out of continuity, unless he has three children, two boys and one girl. But that still doesn't make sense considering he would then have two sons with the same name.
- In Batman Begins Barbara (Gordon's wife) is feeding the infant James Gordon Jr. (James and Barbara's son) while Jim is talking to Batman.
- In the Dark Knight his son also listed as James Gordon Jr. is much older (about 9 or 10) and appears to have a sister. But considering the events in the Dark Knight are about a year after Begins, James couldn't have aged 9 years older.
I don't know. Just a small continuity error that all sequels have. I can easily look past this one.
As far as I can remember, the novel only refers to Gordon's daughter, not to a son at all. I'll look into the credits on Begins, but I don't remember the baby being credited at all...