Alternative Character Interpretation: Schools sometimes use this story (since it's actually not that gory or even hard to comprehend for younger audiences) to teach this trope. Some examples include:
Is Brom Bones a vindictive bully who played a nasty trick on a harmless, lovestruck nerd, or a down-home, all-American good ol' boy who gave just deserts to a venal, manipulative coward? There is a strong modern trend to make Ichabod Crane be actually a heroic character, while Brom Bones is regarded as at best a Jerk Jock — which are both far from Irving's intention to have Bones be the hero and Ichabod a superstitious wimpy moocher Asshole Victim.
The Horseman: a "Scooby-Doo" Hoax by Brom Bones used to scare Ichabod away, or a real demonic figure back from the dead to haunt the forest?
Some food for thought here on both sides of the argument. Earlier in the text it is said the Horseman is riding looking for his head. Meaning he doesn't have a head. When Ichabod sees the Horseman he believes he is carrying a head that he throws at him. Afterwards a smashed pumpkin is found — all of this seems to indicate Brom dressed as the Horseman to scare Ichabod off. However from the other angle the Headless Horseman has no head, meaning he has no eyes. He certainly can't see too well if he was real. We can't undermine the abilities of the horse there either. The pumpkin is seemingly used as a projectile, which it succeeds in getting Ichabod off his horse. This is a pretty good soldier-like move, something the Horseman was. And after all, his own head was taken off by a projectile! But then again Brom could also have hidden his head and used the same strategy as he was described in the story to be 'skilled at horsemanship' (thus able to ride a horse even if his sight is impaired by a piece of cloth or such), strong and mischievous.
Also due note when we hear about Ichabod in New York, he has picked up a lot of ambition since leaving Sleepy Hollow. All throughout the story Ichabod is very much more a laidback guy going from house to house seemingly content with his lifestyle. He even has an excuse as to why he moved which seems a bit convenient. As perhaps New York Ichabod isn't Ichabod as he once was, but the horsemen with Ichabod's head.
For that matter, even if it was Brom, did he really just scare Crane off, or use the locals' belief in the Horseman to get away with a much darker manner of disposing of his rival? As such could New York Ichabod doesn't sound like Ichabod because it's a fake story.
At least one adaptation had it both ways: Bones tried to scare off Crane as a fake horseman but gets knocked out in the process, only for the real Horseman to show up!
One thing that's rather interesting — Disney actually has it rather faithfully, although playing Brom Bones's villainy up a tad more, making it seem like The Bad Guy Wins. But at the same time, try watching it with an adult perspective. As Doug Walker points out in his "Disneycember" short covering the adaptation, Ichabod is actually kind of a dick, helping a baker just so he can pilfer one of her pies and being quite explicitly interested in Katrina because of how much money and food he can enjoy after marrying into her wealthy family - he even has an Imagine Spot in which Katrina's father disappears, leaving behind all his gold rings, shiny buttons and other bling, and Ichabod appears in his spot, now wearing his bling.
An actual canon case of this is in the 1999 CGI film "The Night of the Headless Horseman"; here, Katrina, usually depicted as more or less an innocent caught up in the Love Triangle, is quite blatantly revealed to be egging on both Brom and Ichabod for her own amusement, waiting to see who will ultimately prove worth keeping. And then there's Brom Bones, who is unquestionably the villain, as he makes a Deal with the Devil for Ichabod to disappear.
Depending on your interpretation of Ichabod's motives, combined with Values Dissonance: Is Ichabod kind of a creepy old lecher who is trying to butter up a teenager in order to marry her for her father's wealth? Did he have it coming? This of course depends also on the adaptation, where age differences might be less pronounced and the characters portrayed in more and less sympathetic lights.
Another one is that it was a "Scooby-Doo" Hoax, but it was done by an unnamed third suitor to Katrina - whose plan was to kill Ichabod and frame the murder on Brom Bones. The text mentions that Brom Bones laughed at the incident nervously in the later years - implying that the townsfolk did suspect that Brom may have had something to do with Crane's disappearance. Of course, since the text seems to imply Brom is responsible, could this be an attempt at an Unreliable Narrator attempting to smear Brom in hopes of getting him imprisoned?
Katrina herself. Did she genuinely love Brom or Crane, or did she just enjoy manipulating them? Even the Disney version, surprisingly, leaves itself open to the interpretation that Katrina isn't exactly a paragon of virtue.
Hilarious in Hindsight: Mr. Irving at times admits he made stuff up, such as admitting his inspiration from older tales mixed into the new world. But oddly enough there are some coincidences that have been uncovered that could be cited to make it seem like the ghost story of this tale was authentic but it's more likely they are nothing but hilarious coincidences. Specifically a revolutionary war battle record did indicate the death of a soldier and his horse via canon fire. And if they had been given a group burial they would have been buried in the graveyard where the fictional Horseman rides out from.note At the time group burials from warfare did happen but sometimes were more partisan. Meaning some areas may have just scooped up everybody, others only their own fallen. As of reporting it's not verifiable to a degree most histrionic sources would like whether that did happen on that specific battle. If it did, the burial would most certainly have been there though. While many towns have always had their ghost stories, there's little evidence at all that this actual event had influence on Irving or was linked to any purported haunting before this tale was told. In fact Irving seemed more under the belief he was Americanizing a German legend he knew about in writing this story. The general idea that there would later be an account of an individual to fit Irving's ghost near North Tarrytown/Sleepy Hollow is at least funny. Of course, these are common and vague coincidences (cannons weren't a rarity in war, nor death by cannon, nor death to the solider and horse) and don't entirely add up to any major commotion. Let's just hope that guy's ghost doesn't try some Defictionalization on tourists, or townsfolks in his name either!
Nightmare Fuel: The ending of the 1999 CGI film "The Night of the Headless Horseman". Our In-Universe narrator reveals he is Brom Bones, who made a Deal with the Devil to have the Headless Horseman carry off Ichabod Crane. But, after getting what he wanted, he has to pay back the debt, and so he explains now he has to become a replacement Headless Horseman. Having said this, he pulls his head off his shoulders and lays it on the table, asking his audience/the viewers to "look after it" while he goes and finds a new one. Cue a close-up of the creepy, Uncanny Valley decapitated head booming out an Evil Laugh as the final shot of the film.
One-Scene Wonder: The story isn't even 30 pages long, and Ichabod's entire encounter with the Horseman only lasts 1 and a half pages—but its also the most memorable part of the whole tale.
Signature Scene: The climatic chase scene is by far the most famous part of the story.
Values Dissonance: A modern reader would likely find Ichabod and Brom both equally unsympathetic. Ichabod's essentially a sneering, self-important, arrogant, mooching gold digger, and Brom Bones is a thuggish, anti-intellectual bully. Throw in the hints that Katrina was just manipulating both of them, and you could very well end up with Darkness-Induced Audience Apathy.
Judging by the alternate character interpretation example above, modern readers see Brom Bones a Well-Intentioned Extremist. Especially if the theory of him posing as The Headless Horseman is true.