In the pilot, why was Ichabold arrested and accused of the Sheriff's murder? The Sheriff was killed at a farm, while Ichabold was arrested, literally seconds later, in the middle of the street. Yeah he looked shifty, but so do harmless tramps and vagrants, and being nowhere near the crime scene would presumably prove he wasn't guilty.
When you remember who the arresting officer was, things start to add up.
Why has nobody noticed or mentioned that Andy's body isn't in the morgue anymore?
Why does Sleepy Hollow have so much stuff in it? My home town is about the same size and we don't have a hospital or a police station that big.
In real life, Sleepy Hollow is a town of about 9,000, a bedroom community 30 miles from Manhattan. In the pilot of this show there was a brief shot of a road sign showing "Sleepy Hollow, Population 144,000." Presumably they made it so big partly to justify the police resources.
Actually, the given population is more likely a reference to the Book of Revelations. While it might be their justification for the big police station and hospital, it's just as likely that it's an issue of the writers not knowing how many people buildings that large would service.
Maybe the show's version of Sleepy Hollow has an unusually high demand for police presence and medical treatment, considering the area has apparently been a hotbed of nasty supernatural activity since the Revolutionary War, if not before.
What was the "good" coven's motive for banishing Katrina? Or for killing Ichabod's son after they'd already sent the Golem to purgatory? I feel like they did explain it in "The Golem", but I missed it.
They seem to be establishing that Good Is Not Nice and that the good coven is just as bad as the bad guys in their determined short sightedness. They were pissed at Katrina for not killing Ichabod while he was connected to the horsemen, and they traded her son as part of a deal with the bad guys, and because his powers were getting out of control
In "The Vessel" we find out that there is a militant group gearing up for the end of days and it's hinted at that they are probably a bit crazy and anti-government along the way. Our heroes are fighting the forces of Hell, I think ignoring anti-government types might be in their best interest. Why didn't they invite one of their members along to witness sending a real Demon to Hell? They already told the truth about why they wanted the Lantern and promised to return it, bringing along someone to take it back would just cut out a step. In addition they would gain allies, allies with lots of weapons at least one genuine demon fighting artifact (It wouldn't surprise me if they had a crystal ball they were using as a paperweight) and because of their status as a militia they can't even go public. (Not that they seem to be particularly interested in maintaining the Masquerade and instead maintain it for purely pragmatic purposes. i.e. running around screaming the Headless Horseman is after me doesn't gather allies so much as straight jackets) Instead they at best left then neutral and probably made enemies.
Current American militia movement members are...unstable to say the least. In the short run, maybe they would have been/will be good allies to our heroes. Drag it out, and you don't get pretty results. Even if these guys are justified about the end of the world, how long do you think the alliance would last before the militia decides to stop taking orders and start giving them? Plus, we don't know if they're clued in like the Masons or Sheriff Corbin. For all practical purposes, they could be as useful at stopping the end of the world as a string would be in stopping a semi.
Where did Morales go in "The Vessel"? There's been no indication he's dead, and the demon transferring bodies doesn't seem to knock out the previous host - so what happened to him?
In 'What Lies Beneath' they find an archive of everything they need to know, complete with A holographic ghost of President Thomas Jefferson as a curator who's tangibility changes at a whim. They ultimately decide to destroy it but their logic doesn't hold up. Even if you aren't able to make the correct decision and sacrifice two lives to save the world they manage to save the two lives and then claim that more people will stumble over it. Ignoring that it's remained untouched as far as we can tell for at least two hundred three years the monsters guarding it, Reavers, are virtually harmless by comparison to the other things they've faced. The only reason the heroes were in any danger at all was they went in with two people, with a hand gun and auto-cross bow. If they'd gone back and gotten a few friends with shotguns, rifles and good lights clearing out the reavers would have been just slightly harder than taking out a pack of wild dogs and well worth the risk. If the place had been guarded by something on par with a horseman, or even a powerful witch it would make sense. But Reavers seem respect handgun bullets just fine.
We saw all Four Horsemen in a dream in the second episode of the show. (Granted, the Horseman of War had a slightly different appearance than he would eventually have.) The four white trees were supposed to embody the Four Horsemen. Pestilence was seen in a later episode. Where is the fourth? Moloch has already been defeated, if not destroyed, and the fourth didn't even show hide nor hair.
So, Irving decides to turn himself in so the police won't compare his daughter's DNA with the one on the priest and figure out "she" killed him. Thing is, even with the DNA, who is going to believe that a paralized little girl was strong enough to do that? Not to mention she'd have to stand up to do the deed...