At the beginning of the episode, we learn that the "curiosity" was around in London in 1893. Around 9 min. H.G. says "in the words of my good friend Mr. Doyle: 'the game's afoot'," as she sets out to find the curiosity. Doyle wrote the original Sherlock Holmes stories, the first of which was published in 1890. However, Doyle only ever included the phrase "the game is afoot" in the short story "The Adventure of the Abbey Grange", which was published in 1904.
HG refers to Doyle as "Mr.". Since he was a physician, she should have known to refer to him as "Dr.". If this time frame is set after Doyle was Knighted, she should have referred to him as "Sir Arthur".
In season 2, it was stated several times that H.G.'s daughter, Christina, was killed in Paris in 1899. In this episode, H.G. starts off her narration by stating it was 1893, and that "Christina had been gone for two years."
When Jack and Rebecca arrive at the barn the convertible's roof and windows are all down and the car has a "Continental" spare tire on the rear bumper. When Pete and Myka return there the car windows are rolled part way up, the roof frame is up and the rear bumper is much smaller.
The horn is supposed to have the power to destroy anything in its way yet, when mounted on the parabolic dish, it "fires" at the center reflector without damaging it. Also the reflected sound does not damage the dish.
The photo the adult Daniel has of he and his dad from the 60s (on his monitor) is in 4" x 6" format and has no white border or aging/fading that would typically be found from a color image 50 years old. Even if the image was scanned, cropped and in landscape orientation (most snapshot film of the era was square) then printed there would still be evidence of color fading.
Rebecca claimed in Burnout that she changed her last name to St. Clair when she moved to St. Louis. However, Jack introduced her as "Agent St. Clair" when interviewing Billy and Peg in 1962 and calls her "Miss St. Claire" at the end of the episode.
The 'Cherry Picker' that Myka is referred to by Pete as having ridden up in could not have reached the top of the roof at its full extension. The roof would have been accessed from the interior of the building.