In the book of Genesis, why was Canaan punished for his father's indiscretion? It was Ham who was laughing and making shameful comments about Noah, not his son. It seems that God has a way of punishing future generations for mistakes made by the ancestors. Eve's mistake was punish by women having pain during childbirth. Now Canaan is punished for Ham's mistake. What am I missing? Are the future generations being punished as a constant reminder?
I believe you have a good grasp of the situation, at least in part. Yes, the punishments on the serpent, women, and men do serve as a continual reminder that the consequences of sin usually lead much farther than you might intend. The guy who gets drunk might never intended to kill a small child when he swerved into another lane and hit a car, but such things do happen.
I was reading a verse in Proverbs today that talks about this. "A servant will not be corrected by mere words; for though he understands, he will not respond" (Proverbs 29:19). Words alone don't cause a person to correct his behavior. Words can be ignored. There has to be something more to spur a person to change.
But another reason is that we forget that despite the continual reminders, we behave no better than Adam and Eve did. "Therefore, just as through one man sin entered the world, and death through sin, and thus death spread to all men, because all sinned" (Romans 5:12). Adam opened the door to sin, but we don't close it. Instead we help to keep it open. Therefore, another way to look at the punishment of the man and woman is to see it as a statement of fact. Because of their sin, they brought caused their world to irrevocably to change. God was acknowledging that because they sinned, their children would follow in their footsteps because such is the nature of sin.
"So Noah awoke from his wine, and knew what his younger son had done to him. Then he said: "Cursed be Canaan; A servant of servants he shall be to his brethren." And he said: "Blessed be the LORD, the God of Shem, and may Canaan be his servant. May God enlarge Japheth, and may he dwell in the tents of Shem; and may Canaan be his servant"" (Genesis 9:25-27).
What you are overlooking in the story of Noah, Ham, and Canaan is that we don't know the character of Canaan. But we do know that children tend to imitate their parents. The problem between Noah and Ham is one between a parent and child. "A wise son makes a glad father, but a foolish son is the grief of his mother" (Proverbs 10:1). Ham has demonstrated his foolishness and in response Noah is stating that his foolish is going to continue on through generations. Noah's words are a prophecy that Canaan's descendants are not going to wise up. They will end up serving the descendants of Noah's other sons.
Another way to look at this, is if you ever remember your mother telling you, "Just wait until you have children of your own! Then I'm going to laugh when they treat you like dirt!"
Why wasn't Ham or his older sons mentioned? As I explained in "The World After the Flood," one way to insult someone is to ignore them, but an even greater insult is give them some small token to let them know it wasn't just an oversight. So when a waiter gives you really bad service, you leave a dime on the table. The dime says, "I didn't forget your tip. I thought you didn't deserve one."
When Noah prophesied what would happen to his children in the future, he spoke of Japheth and Shem's descendants, but he ignored Ham and his children. But to let everyone know it wasn't a simple oversight, he mentions only what will happen to the descendants of the youngest (least significant) child of Ham. It doesn't mean that the older children of Ham would fair better or worse, Noah is simply stating through action that he is so angry with Ham that he isn't going to tell him what will happen to the rest of his children. It wasn't an oversight, but he would let Ham know how miserable the life of his youngest son's descendants would be and it is implied that it is because Ham's foolishness would be passed down through the generations.