This list is not complete because I didn't complete all cases on the playthroughs where I was worried about getting all survivors — I'll have it finished soon, since I need to find out some more info on endings.
I also wasn't planning on giving much more detail on these here, since the main story wasn't the intent of this guide. But if people want it, feel free to email me and I can fill it in.
Case 1-1 Starts September 19 at 12:00pm. Ends the first time you leave the Warehouse to enter Paradise Plaza.
Case 1-2 — Backup For Brad Starts when you finish 1-1. Finishes when you defeat Carlito.
Case 1-3 — An Odd Old Man Starts when you finish 1-2. Finishes when you enter the Entrance Plaza with Brad.
Case 1-4 — A Temporary Agreement Starts when you finish 1-3. Finishes when you enter the Security Room.
Case 2-1 — Image In The Monitor Starts September 20 at 6:00am. Finishes at 6:00am (or slightly after) when you arrive back at the Security Office.
Case 2-2 — Rescue The Professor Starts when you finish 2-1. Finished when you defeat Carlito in the Entrance Plaza.
Case 2-3 — Medicine Run Starts after completing 2-2. Finishes when you give Jessie the First Aid Kit.
Case 3-1 — The Professor's Past Starts September 20 at 11:00am. Finishes when you enter the Security office after 11.
Case 4-1 — Another Source Starts September 20 at 3:00pm. Finishes when you enter the Security office after 3.
Case 4-2 — Girl Hunting Starts after completing 4-1. Finishes when you defeat Isabela.
Case 5-1 — A Promise To Isabela Starts September 21 at 12:00am. Finishes when you get Isabela back to the Security Room.
Case 5-2 — Transporting Isabela Starts after completing 5-1. Finishes when you return to the Security Room with Isabela.
Case 6-1 — Santa Cabeza Starts September 21 at 3:00am. Finishes when you return to the security room after 3.
Stop after this case if you want the Saint achievement (unless you are going all the way through Overtime mode, in which case you can continue as long as you have saved every single person thus far)!
Case 7-1 — The Last Resort Starts September 21 at 11:00am. Finishes when you arrive at the Security Room.
Case 7-2 — Bomb Collector Starts when you complete 7-1. Finishes when you get all the bombs outside.
Case 8-1 — Jamming Device Starts September 21 at 5:00pm. Finishes when you return to the Security Room after 5.
Case 8-2 — Hideout Starts when you finish 8-1. Finishes when you reach the hideout with Isabela.
Case 8-3 — Jessie's Discovery Starts when you finish 8-2. Finishes when you arrive back at the Security Office.
Case 8-4 — The Butcher Starts when you finish 8-3. Finishes when you defeat The Butcher.
The Facts — Memories Starts September 21 at 10:00am. Finishes when you are at Isabela's hideout at 10:00am.