When Helen is first admitted to the mental hospital, she screams that Candyman is there. The doctor & the orderlies rush in and give her medication. When Helen & the doctor view the security camera later, the events & dialogue are out of sequence.
When Helen goes back to save the baby she originally has on black shoes but when she climbs through the wall, her shoes are blue.
Helen has a bath after returning from the police station, she gets out and her hair is wet. She looks at some of the slides she took, seeming to take only a minute or two to do this, and then turns off the machine. When she stands up to open the curtains, her hair is perfectly dry.
Despite the fact that Helen has been in the mental hospital over a month, her hair is no longer than it was when she was admitted.
When Helen and Jake begin walking towards the public toilets, it is overcast, then when they pass the bonfire stand it is sunny with bright blue skies. When they arrive at the public toilets it is once again overcast.
During the course of the movie, we hear bells release classes and we see lockers. "Candyman" is set at a university, so there wouldn't be bells or lockers.
Helen discovers the blurry outline of Candyman in the photo of her shooting her own reflection in the mirror. The focus of the photo is on her reflection. She then changes the focus of the projector and it sharpens Candyman's outline. This is impossible, since the slide is a 2D-representation with no depth information.
At (approximately) 61:46, Helen asks Trevor to hold her, and he embraces her. The police would not allow this, as it would contaminate any evidence they can get from her body and clothing.
Although forensic evidence gathering and especially the use of DNA evidence is not as advanced as it is today (or even a couple of years after this film's release), detailed examination of the scenes should point away from Helen.
When Helen is clicking through slides after taking a bath, she views two slides of the painting of Candyman's face with the hole in the mouth. Earlier in the movie, she had run out of film before entering that room. However, she is later seen going back to take pictures of it; this is right before she meets the little boy, Jake.
64 minutes in, when Helen is having a medical injection, the needle bends on her shoulder.
When supposedly recording the student's Candyman story at the start of the film, Helen's dictaphone is actually in the playback position - the record button isn't pressed down.
When Trevor arrives home (when Helen is preparing dinner) she points to her left eye and reveals it is much better. Both of Helen's eyes are a blueish green throughout the film, but when she points at her eye in this scene she is wearing a brown contact lens.
When Stacey cuts her finger preparing dinner, we hear her "Ow" before her lips move.
When the Candyman breaks the window to escape the psychiatrist's office at the hospital, the wire pulling him through the window is visible.
No one prepares a bonfire a month in advance, especially in an impoverished urban area. It would invite rats, cockroaches, and other vermin to have junk out that long.
Trevor explains away Helen's annoyance at his lecture on urban legends tainting her research as having to follow the curriculum. That isn't how higher education works, and no professor would ever talk like that, and no professor's spouse (who is also in academia as a graduate student) would accept such an answer. "Curriculum" is which classes are required, and what BASIC topics will be covered in a class, but professors absolutely have academic freedom to choose specific topics and the order they are presented in their class. Professors do not follow specific curriculum rules (or even guidelines) like PreK-12 teachers are forced to use.
Helen and Bernadette's research seems more appropriate for doctoral work than for a master's thesis, which may have been what the original author intended. After all, the author was British, and the British refer to doctoral dissertations as doctoral theses (Americans do not). When they switched the setting to Chicago, they really should have switched all of the "thesis" references to "dissertation."