What is the evidence that memory is constructive, rather than being like a tape that we just replay?

Answer 1

Try this: Ask your friends and family what they remember about the attacks on the twin towers. Think about your own memories. Record it all, and then review the news articles about the incident. You'll see that everyone's memories differ from one another's and thus differ from that which actually happened.
Part of the reason is because each individual has some sort of emotional response to what happened, perhaps some prejudices, etc.
Some psychologist suggest that vivid, photolike flashbulb images may actually represent our tendency to go back and fill in the details of an event after the fact. This theory makes sense if we view memory as a constructive process in which information we have already stored affects the way we remember an event. From this perspective, our information processing is not limited to efforts to store facts as accurately as possible. Rather, we frequently add or delete details to make new information consistent with the way we already conceive our world. Thus remembering is often a process of mentally "reconstructing" an event rather than simply searching long-term memory for a perfect copy of it.
Another example: If you recall any event in your life, major or not, and ask all those involved in the memory, you will find that they either don't remember it the same way, or they don't recall it at all. My sister has pretty accurate memory, where she can remember even the tiniest of details (such as the color of the carpet, the way a person stood and looked, what everyone was wearing, etc.) Some people have memories of things which never occurred in the first place. Their minds have "constructed" details and memories of things they think happened, according to how they perceive their world. Some people remember things that others simply do not. It's a constructive process which each individual operates differently.

Answer 2

Most new inventions and/or ideas are constructed from pieces of memories you already have, even those from your imagination.
One downside is that we sometimes invent our recollections to suit our own agendas, prejudices, etc.