I think this things may be good:
1. Some kind of detective work: searching and collecting pieces of evidence, questioning witnesses, etc. Questioning may be realized as rudimentary RPG-like dialog system.
2. Two selectable modes: detective/agent/operative/how-it-called-in-your-country and patrolman. The first mode is for serious calls like homicides, robberies, firefights-in-progress or after ones; mostly actions that suggested in section 1 and/or assisting patrolmen in tough situationg. Second mode - street fights, traffic violations, first response for 1-st mode situations etc. Also there can be mixed mode (or smth like that).
3. Possibility to use civilian outfit and/or car (unmarked/undercover). As I know there is nice mod "Dash Light Mod" by Luxart that can be useful. Also ability to show badge/ID while undercover.
4. Rare but interesting and challenging calls like bank robbery, terrorist attaks on government buildings, major drug operations, you know...