When Wednesday is talking to Enid on the balcony, about her pet scorpion, her arms go from crossed to her sides as the camera angle changes.
At the beginning of the scene in the Weathervane cafe, Wednesday's lipstick is a subtle skin tone. It later changes to a much brighter red colour.
Sirens do not have scales and have no particular fondness for water, you're thinking of mermaids.
Sirens live by the sea, mermaids live in it.
Teenage Wednesday has a chin dimple that her younger self, shown in flashback, lacks. A chin dimple is caused by improper fusing of the jaw bone in early development and is not a trait that changes as one ages.
When Thing goes to Tyler's house to tell him to FaceTime Wednesday, Tyler pulls out what is clearly supposed to be a metal baseball bat to attack Thing. However, in the shot where Thing grabs the bat, it is clear that it is a normal wooden bat that has been painted silver.
At fencing practice, Wednesday suggests a match with no masks and no tips. Whoever draws first blood wins. She and her opponent remove their masks, but do not remove the tip guard from their foils (if they have removable guards) or switch them out for live blades, yet the blade still cuts Wednesday's face.
Technically, the stone creature that plunged off the roof towards Wednesday was not a gargoyle. A gargoyle is always a water spout used to channel water from gutters away from the walls of building (which is how it got its name, the water "gargles" from it's mouth). The sculpture is actually a grotesque.