For the first film: Why did Eric and Shelly's apartment still have police tape over the front door one year later? Police investigation of the scene should be long since done. I can understand there being no interest in fixing the place up and renting it out again, but over the course of the year there hadn't even been a single prospective squatter or looter who would have torn the tapes off?
As far as squatters go the whole reason they were murdered was for resisting Top Dollar's attempts to remove everyone from the area. It's reasonable then that no one would have returned to live there, even illegally. However the tape should have still been removed after the scene was opened at the conclusion of the police investigation.
They lived in the extreme slums. What makes you think there 'was' a police investigation? They showed up to drag out the bodies, put up tape, dragged out the bodies, never came back.
Related to the above, how did Gabriel the cat survive the entire year, with no visible changes? The police apparently didn't notice him during their investigation, and Sarah thought he'd died, so there was no one to feed or take care of him. It's possible he traveled outside to hunt via the window? But when Eric comes back, he finds his same friendly, plump, pristine white, long-haired cat, rather than the underfed, terribly matted semi-feral Gabriel more likely would have had to become.
Maybe the crow wasn't the only magical animal. Gabriel is an all white cat and didn't seem bothered when his long dead owner returned. This troper had always assumed that Gabriel was supposed to be an angel or something along those lines but that it was scrapped or not given that much emphasis.
As the crow (the bird, I mean) was seemingly killed, or better yet, injured, Eric not only lost his regenerative abilities, but also began bleeding from his injuries. Does the crow's absence mean that Eric is alive once more(animation via vulnerability), or just loss of his power?
In the deleted scene with the Skull Cowboy, Eric actually lost his powers when he killed Skank. Even ignoring that, as the next two films show, the Crow can't really be killed and it just weakens the person it returned.
T-Bird reports to Top Dollar that Eric killed Tin-Tin by stabbing him in all his vital organs "in alphabetical order." How could he know what order each organ was stabbed in? Was he hanging around watching? (I always presumed that this was a metaphorical embellishment for poetic emphasis. Like one might say "from A to Z" or "six ways to Sunday".)