I'd like to know about examples of prominent scientists having exceptionally good memory, with anecdotes if possible, and how it affected their work. It would also be interesting to see examples of the complete opposite, prominent scientists having exceptionally bad memory, and how they made up for it.
The standard example of "complete opposite" was N. Wiener. Anecdotes:
Wiener walking on campus is stopped by someone and they start a mathematical conversation. After the end of the conversation Wiener asks: "In which direction I was walking before I met you?" -"This direction." -"OK, this means I already had my lunch!"
Wiener bought a new house. On the way back home from his office, he forgot where it was. He sees a little girl and asks: "Do you know where the Wieners live? They recently moved to this neighborhood". -"Yes, Daddy! My mother sent me to meet you!".
A student comes to the post office. He sees Wiener walking back and forth, in deep thought. For some time the student hesitates to distract him, but finally addresses him: "Professor Wiener, ..." -"Oh, yes! Wiener! (Addressing the post office clerk) Wiener! Do you have something for Wiener?"
As an example of good memory, Hardy surprised his friends by remembering all cricket scores for many years.
Speaking seriously, from what I read and from my own contacts with outstanding physicists and mathematicians, I can conclude that ability to do original work in science is not correlated with good or bad memory. Like it does not correlate with body weight or height. Unlike weight and height, memory cannot be objectively measured because it is highly selective. (A person may remember cricket scores for many years but poorly memorize verses etc.) Experience shows that this kind of ability simply does not correlate with the ability to do exact sciences.
There are similar stories about Einstein. There are two sides to this. On the one hand: all people, even geniuses, have problems with their memory when they get old. On the other hand: Both Wiener and Einstein were outspoken critics of the cold war hysteria. These stories were part of an agenda to depict them as harmless eccentrics whose opinions on political and ethical matters did not need to be taken seriously.