If a woman becomes pregnant while on the pill and doesn't realize it still taking the pill, will it harm the baby?

Unlikely: The pill manufacturers all give the precaution "do not take this medication if you are pregnant". About 1 to 3 % of women on the pill still conceive. Those pregnancies are no more likely to have any specific complication than unexposed pregnancies. While there are no specific studies showing safety or harm - it does not appear from those exposed pregnancies that there is any particular harm.