I think one interesting way to look at the connection between monuments and memory is to examine the controversies that some have led to. For example, the Vietnam Veterans Memorial was at the center of several different controversies. It's abstract design was criticized, then later its lack of an American flag, and omission of women. The second two issues were addressed by the addition of two statues. This website describes some of the history of the memorial, including the controversies. Although it is not from a completely objective view, it seems to have a good summary of what happened.
Controversies over monuments such as the Vietnam Veterans Memorial show that the way we choose to remember events and people often involves conflict. Monuments can serve as reminders and commemorations for those who experienced the event, and as places to learn about the event, and those involved, for those who did not. They symbolize the way we choose to remember something or someone as a group, and how we want those who come later to see them or it.
Another example of this is the FDR memorial. There was controversy over whether he should be shown in a wheelchair. Because he had hidden his disability during his presidency, it was thought that he would not have wanted to be remembered with it. However, some wanted his wheelchair to be shown, as it would show how he overcame difficulties to become a great leader. In this case there was a clash between the wishes of the person being remembered and those wanting to remember him. The issue of historical accuracy was also raised.
I don't think memorials are meant to be a faithful document of what really happened. They are there not only to preserve our memories, but to shape them. They allow us to share a certain group version of what happened and why it was important.