Factual error: In the opening scene when the men in orange sashes are greeting each other, you can briefly see one of the men in an orange sash wearing what are quite obviously modern sunglasses. Even if the glasses were meant to be from the period, sunglasses were not mass-produced or widely available until the late 1920's.
Continuity mistake: The snake that bites - and therefore kills - Prof. Greenwood (and which is later found by Crabtree and Higgins) has nothing to do with the one Dr. Bajjali puts on her shoulders or the one Dr. Grace dissects later on, despite they are supposed to be the very same snake. The first one is seemingly a King cobra, while the other one resembles a Python (which is not even venomous). The visual difference is totally obvious.
Stroll on the Wild Side part 2 - S5-E8
Revealing mistake: Towards the end of the episode, when Murdoch attacks Falcone, look closely: the first punch - which knocks the mob boss down - looks convincing but the second time Murdoch "hits" him, he punches nothing but the ground. Falcone is facing right while the detective strikes his left side, at least an inch away from his head.
Murdoch Night in Canada - S5-E12
Other mistake: Murdoch sends Crabtree to buy six pumpkins, but when they test how tall the murderer might be, there are much more pumpkins can be seen.
Answer: It's certainly a personal choice about using one, and probably similar to how some people refuse to wear a helmet or forego other safety equipment. Most bells and horns on bikes are not very loud and probably wouldn't be heard in busy traffic, making them mostly ineffective. Murdoch would likely still yell, even if he had a bell or horn.
raywest ★