Based on the overcoats Briscoe and Curtis wear, it must be late fall or winter. When they enter an apartment at 6:15 am, the sun is shining through a window, although the sun likely wouldn't be up that high at that time. When they check a car minutes later, it's raining.
The bayonet was describe by the seller as a "Korean War" type, but the Korean War bayonet for the M-1 (Garand) rifle was much shorter. This looks more like a WW1 (1903 Springfield) bayonet.
At the crime scene, a chalk outline from one of the victims is seen on the ground. Such a thing isn't done, because it contaminates the scene.
When James Smith is being chased through the library, he knocks over a rack full of books. The books remain attached to the rack as it falls over.