"Microstamp"?
In one of the episodes, the FBI ties the cartridge case that they found in the arcade to a specific gun via the "microstamp" that the gun supposedly left on the case. This leads them to Darlene, because the owner of the gun said she stole it from his safe.
The problem is: "microstamping" technology has never been used on any production gun; not once, not ever; let alone used on a cheap Charter Arms 79K that was last manufactured in 1996, which is before the concept of "microstamping" even existed.
California (and only California) passed a blatantly unconstitutional law in 2007 requiring "microstamping" on all new models of automatic pistols, so gun manufacturers simply stopped selling new models behind the iron curtain, because it's an infeasible requirement.
In other words, it was utterly impossible to tie that cartridge case to the gun that fired it. They could potentially match the case to the gun if they already had the gun, but they didn't. They looked into some fictional "microstamping" database and it spit out the name of the guy who bought the gun.
Also, disposing of a body in a pet crematory? No one noticed the human bones that were left over? Contrary to popular belief, the body isn't completely reduced to ashes in a crematory furnace. After the incineration is complete, the bones are removed from the furnace and put into a machine where they are pulverized into an ash- or sand-like substance.