When Kolchak is telling Vincenzo about prior murders, he states one set occurred 52 years before. When Vincenzo repeats that back to him, he says 53 years instead.
The days and dates are continually inconsistent. The professor's comment that 2027 is "52 years from now" sets the story in 1975. The narration says that the football player was killed on "Monday, September 22", which was correct for 1975. The soldier was killed on "Wednesday, September 29", which is incorrect for both 1975 and any year when the 22nd is on a Monday. At the end, when Kolchak looks at his watch, it shows Monday the 25th, which is incorrect for both 1975, the story in general, and also is four days before the date given for the death of the soldier.
Kolchak talks about Venus appearing at 12:10am. However, the earliest that Venus can ever rise in Chicago is 3 hours 51 minutes before sunrise, and the earliest the sun ever rises in Chicago is at 5:15am (on mid-summer's day), so Venus is never visible in Chicago at 12:10am.
The fall of the Aztec Empire was not in 1507, but actually happened in 1521.
The soldier killed at the beginning is said to be a Staff Sergeant, but is wearing sleeve insignia of a Specialist First Class. Also, he was supposed to have been awarded the Distinguish Service Cross and that chest ribbon is not present.
Kolchak is asking Vincenzo to sign a voucher for the taxidermy specimen he bought to get the information, saying it cost $24.75. The price tag on the item reads $19.95 (on sale). Kolchak is trying to get $5 extra from Vincenzo.
At the very end, just before the fade-to-black, on the close-up of the mummy's head, the actor opens his eyes and blinks.
The dispatcher announces that a "1-8-7" has occurred.
California Penal Code Section #187 covers homicide. The penal code section for Illinois (the setting location of series) is not the same.
As a police car is driving down the street, a Union 76 service station is seen in the background. Union 76 (the former Unocal) never had locations in the Chicagoland area. The show is filmed in Los Angeles.
Early in the story, Kolchak is supposedly driving in Chicago, but he's plainly on Melrose Avenue in Los Angeles, passing the famous "RKO globe" on the southwest corner of the Paramount lot.
Each victim has to be killed on higher and higher flights of stairs. The victim, Lyons, is never shown to have been sacrificed on any flight of stairs.
The Air Force officers that Kolchak is introduced to at the hotel never remove their hats while indoors, despite not being "under arms" (carrying a weapon or wearing a weapon belt). This is a serious uniform violation.