The only plothole I found in the OT was having Lukes last name the same as his fathers, when they were trying to hide him!
Leia was Leia Organa, so unless Vader sensed her, he would never suspect her to be his child. Now he hears about Luke Skwalker, who is 20 years old, and Vader remembers impregnating his wife 20 years ago.......put 2 + 2 and it equals 4.
Yes but he doesnt discover Lukes name until the ESB when the Emperor explains what he wants Vader to do.
Emperor: "There has ben a great disturbance in the force....we have a new enemy, the young rebel who destroyed the Death Star. I have no doubt that this boy is the offspring of; Anakin Skywalker."
Vader: "How is this possible?"
Emperor: "Search your feelings Lord Vader. You will know it to be true."
Something like that............lol This help?