Sounds like Psych on the USA Network. He would do something similar.
As for the OP's question, if a player is will do make the feat investment and it doesn't hurt the other players, I'd totally allow it.
This is especially true if the player comes into new information to help contextualize or better inform how what they have scene fits into the question or challenge they face.
Unforgettable was the tv series, starring Poppy Montgomery who was also on
Without A Trace.
[voice-over at the beginning of each episode]
I'm Carrie Wells. Only a few people in the world have the ability to remember everything. I'm one of them. Pick any day of my life, and I can tell you what I saw or heard. Faces, conversations, clues - which comes in handy when you're a cop. If I miss something the first time, it's okay - I can go back and look again. My life is unforgettable.
The feat allows you to perfectly recall anything you've seen or heard in the past 30 days. The investment of character resources in a feat is a big deal, and should allow the character to do some pretty shiny things in the right circumstances. The mind stores a great deal more information than it fully processes on a conscious level, so I'd certainly allow a character who took the feat to revisit a particular moment within that time period as though they were physically right back in that moment, and make an Investigation or Insight check to better interpret their stored sensory input.
Obviously, the Investigation check would work in slightly different ways in different situations. There are three ways I can think of in which allowing a character with Keen Mind to investigate their own memories would work - general knowledge, analyzing a specific situation/moment, and trying to analyze their entire memory to put clues together...
- On a general note, the DM should be throwing the player a bunch of minor bones on a day to day basis - the character always remembers important plot information, the names of people and places the player himself forgot about, doesn't get lost in any place that he's been before, and sometimes the need for an Investigation check to pick up general information (locating a blacksmith, finding a place to stay, which way to the docks, etc.) can be sidestepped by simply telling the player that the character recalls having seen or overheard something - a hammering noise heard a few streets over as they passed, someone in the market telling a someone else they ate at the Candlekeep inn on the West Side last week, or the flash of a top sail over the top of a building as they walked up the hill to the castle...
The DM can also use this type of thing as an opportunity to feed the party information, clues or plot hooks, either through a passive Investigation check or simply by informing the player that their character's super-sponge brain has picked up enough background noise to put together a relevant thought about something.
Making an Investigation check to see if the character can fish some general knowledge out of their recollections shouldn't take more than a minute or so.
- If a character wanted to make an Investigation or Insight check to analyze a particular memory in order to try to glean new information from it that they didn't get when it originally happened, it would need to be treated just like it was when they were there the first time.
The major caveat, though, is exactly that - the character is
physically reliving that moment, and thus limited to the character's physical sensory input. If the character was standing in front of the Guard Commander's desk, they could certainly recall the entire list of titles on the bookshelf behind the desk. On the other hand, if the character was standing twenty feet away in the back of the room at the time, the books would have been too far away to see the titles on them. If the character never searched the room, they'd only be able to recall what was in plain sight - they could recall the location of every piece of furniture, every object and every person in the room, and they
might notice the scratches on the floor left by the secret door behind the bookshelf, but there's no way they'd be able to know about the loaded hand crossbow under the desk since there's no way to see it from the other side.
(Unless perhaps the character has asked to make an Insight check on the Commander and the DM decides that a successful Insight check reveals that the Commander's body language gave away that he was contemplating reaching for it.)
A check to gain any sort of new general information or insight on the situation would take at least a minute. It would very much depend on the particular situation what new information or insight the character gleaned and the relevance of it - failure probably means the character realizes the Commander has forgotten to water the plant on his desk. The player would need to ask the DM specific questions in order to get more than just general answers, and
each question would probably take at least one minute.
- Finally, if the character with the feat is trying to troll through their
entire memory in order to find clues or connections between facts/events/etc., it's going to be entirely up to the DM to decide whether or not there's anything to be gained from it, and if so, how much, since it's essentially a fishing expedition. An attempt to go all full-on Sherlock Holmes like this should probably require that it be done during a long rest.
