One common plot point is the emotional reunion between Harry and his parents. There's often a lot of crying and hugging. Another is how Harry's parents deal with the people who abused Harry. They might seek revenge or at least make sure those people can't harm Harry again.
In many 'Harry Abused Parents Return' fanfics, a common plot point is the adjustment period for all the characters. Harry has to get used to having his parents back, and his parents have to adjust to the new wizarding world that has changed since their death. There's also the aspect of how the return of his parents affects Harry's relationships with his friends. Some friends might be happy for him, while others could be jealous or feel left out. And of course, there's the overarching plot of how the family unit now deals with the ongoing threats in the wizarding world, whether it's dark wizards or the Ministry's politics.