I think that we're going to see some pretty significant differences with many of the main characters in the new 2004 timeline. These differences will give us some hints about how much of a role the Island had in these character's lives. Here's some guesses as to how people will be different. Some of this is based on hints we saw in the premiere, but a lot of this is total guesswork based on what might make an interesting story.
We saw that Jack is still a surgeon, and is still bringing his dead father home. This time, he had a good relationship with his father who had been somehow involved with the Island in the original timeline.
Locke never met Cooper. His spine was injured in a different accident. He never met Helen and actually did go on the walkabout like he told Boone.
Rose and Bernard are very similar, but Rose either doesn't have cancer, or was cured by the faith healer. They seemed much happier.
Sawyer never wrote that letter because Jacob didn't give him the pen, and let go of his parents death. Since he wasn't obsessed with Sawyer, he did not become a con artist. He's possibly in law enforcement.
Boone and Shannon had no romantic relationship. Shannon's father is not dead and she has healthier relationships with men.
Jin works for Paik. He is escorting Sun, the boss' daughter, to America to meet a man that her mother is trying to matchmake her with. He is trying to steal money from Paik and run away to America. He's learned English. He tells Sun to button her top because he works for Paik, not because he's involved with her. Sun never learned to speak English because she had been only motivated to do so in order to escape from Jin.
Sayid did not become a torturer and never met Kelvin. His recent past is still similar, but he met Nadia under different circumstances.
Charlie and Claire have almost the exact same backgrounds and motivations.
Desmond never met Penny and does not have a chip on his shoulder about Widmore (who may be dead). He has worked a series of odd jobs and drifts, and doesn't really feel like he has a purpose.
Michael's wife never left New York. She, Michael, and Walt are all still living there together.
Juliet's ex-husband was not killed by the bus. She has the same research position and is under his thumb. She'll meet Sawyer soon and suggest that they go out for coffee sometime and can go Dutch.
Charles, Eloise, and Richard all died in the blast. Daniel was never born.
Miles and Charlotte got off the island. They have had very similar lives.
Kate & Hurley: I'm not going to make predictions because my guesses are based on the Comic Con videos and may be considered spoilers. Kate's changes will result from her not getting the lunchbox/time capsule, and Hurley's changes will result from the numbers having a very different meaning.