Snapshot

A Snapshot is a "replay" of a past point in time. A couple of "real detectives" can go back into the snapshot to observe what happened. However, since they are active participants, they can create "deviations" from the actual events. The snapshot computers provide a fully accurate replay of a small region. They also are able to calculate the degree of "change" that occurred in the snapshot. However, only "real people" in the snapshot can observe the details. The real people can also suffer and die within the snapshot. They can't really bring anything out of the snapshot. (Though they may be able to swallow something.) There are also plenty of privacy concerns with Snapshots. They can only be explored under warrant. The snapshot detective positions are low prestige, and typically takes those with minimal other opportunities. In a Snapshot, however, they are near omnipotent. They can flash a "snapshot" badge which lets people know they are in a snapshot, causing interesting reactions.
The Snapshot story follows two partners who are on duty to try to hunt for a murder weapon. They are able to find that, and then are told to stay in a safe house while waiting to explore a domestic violence incident. However, rather than do that, they explore another case of a serial killer that seems to be working around snapshot detectives. They also take time to visit family including one detectives non-custodial child. Things take a few turns, and we also end up with a Snapshot in a Snapshot and a few murder cases being resolved.
The snapshot is an intriguing structure. The story explores a lot of the concerns and abuses. It is also set as a "one burst of technology" in the near term future. There is a great deal of opportunity to explore this technology in future work.