Other mistake: The entire Buddha structure had tip over onto its side yet the bowl and its pedestal inside the structure remained the right way up ready for Sydney and Nigel to come and find it.
Smoking Gun - S1-E2
Other mistake: The episode begins with a caption; "Chicago, 1930." In present day, through internet magic (hotel records from early 1900s somehow digitalized and publicly available!) Nigel and Sydney talk about the history (fictional, no actual historical basis) of the Roxbury. Nigel says that the original owner went out of business "after the war", then the company was sold, and the hotel refurbished, despite being, Sydney says, "only 5 years old." Later in the episode, Sydney looks at a plaque from the Chicago Historical Board that dates the elevator as "circa 1901." (00:12:35)
Smoking Gun - S1-E2
Other mistake: Somehow, the pineapple grenade that explodes right against the room's baseboard punches a hole in a thick stone wall, but in the middle of it, preserving the base and creating a gap in a diamond shape that radiates from mid-height. (00:17:40)
Other mistake: When looking for the floor where the diamond is cut Nigel sees a sign which he translates as "Brown Duck." The sign however is misspelled Bruin Eend Kleren. In Dutch it would have to be Bruine Eend Kleren. (00:37:25)
Other mistake: In the Romeo & Juliet-like beginning of the story, Calum looks at his own hand and discovers Elena's blood. Obviously censorship ratings prevent the scene from being realistic and he has barely a smudge of blood on his own hand, but Elena was lying dead on top of him; the fact that his clothes are absolutely pristine for the rest of the scene is laughable - at least she could have gutted herself a little bit on the side and not where she would inevitably bleed him a river right on his white shirt. (00:02:55)
Other mistake: Calum fights off Elena's father and is chased away by the guards. Somehow he has a fight on the top of the stairs with 2 guards, but it takes in excess of 40 seconds for the previous pursuers to catch up with him. (00:04:25)
The Legend of the Lost - S2-E4
Other mistake: When the bad guy at the start of the episode runs to chase Sydney and Nigel, his foot kicks the side of the large stone lid which cause it to lift up. If this large piece of stone was real stone it would not have moved at all from being nudged by a foot.