[Terizent]

Welp, that could work. October 5th 2112 would also be a Wednesday, so taking that into account, our current timeline would look like this:

October 4 2112-Akane's first day at CID. Random rapist is killed. Episode 1.
October 5 2112-Akane's second day at CID. Episode 2. Additionally, Talisman is murdered and flushed down the toilet.
Sometime during October-CID investigates a drone factory. The month is shown in a graph. Episode 3.
December 5 2112-2 months after Talisman's death, the CID investigates his house. Episode 4.
----Sometime in the night between these two dates, Spooky Boogey is murdered.
December 6 2122-The case continues into the next day. Midou is killed. Episode 5.