Sitting down to write a review of Monster of the Week while being a guy who can't abide essentially any episode of Supernatural you care to name, and who only really liked Buffy: The Vampire Slayer for the side characters is an exercise in trying to refocus on "but is this really FOR me?" Let's at least step back a little and try to see where this work fits in the history of the genre.
While episodic action-adventure shows have been common on television since the earliest days, the combination of horror, episodic enemies and recurring protagonists first came about in the cartoon Scooby-Doo, Where Are You! in 1969. Before that time, episodic horror was the realm of the anthology series (Alfred Hitchcock Presents, Thriller, etc.) or the soap opera - always an innovator in television (Dark Shadows). The Scooby-Doo formula would be refined in more standard dramas like Kolchak, The Night Stalker, and was a consistent theme in cartoons like The Real Ghostbusters. The formula is this: The characters, intertwined in various ways, with strong relationships and connections to each other, face a supernatural evil. The evil grows in intensity, the characters face setbacks and attempt to save each other and the world, and ultimately the (seemingly) supernatural evil is defeated, and the characters return to the status quo. The classic show that combined the episodic and the serial in this field was Buffy The Vampire Slayer, which ran for seven seasons on TV and another five in comics, which attempted to make the relationship web of the characters more serial, while the episodic threats were loosely connected, the characters facing a "Big Bad", as they self-referentially called it, at the end of each season.
At its most successful, BTVS was able to transcend the formula, but it often did so in ways that displayed the weakness of the formula itself. When BTVS elevated its supporting cast, it showed the web of deep, interwoven relationships that had developed over the seasons, and the changes the characters had gone through - like a serial show, like a soap opera. When it played with its own presentation (a silent episode, a musical episode) it showed how much greater range its performers had than the formula really required of them. While incredibly influential and successful, BTVS actually had threaded a very tight needle. Followups (Angel, Supernatural) seemed unable to replicate this, with good reason.
The monster-of-the-week genre is one that, ironically, the RPG hobby had developed far more aggressively and in-depth than television had. Call of Cthulhu's module play often emphasized the idea of the location-based scenarios - investigators came to a place, summoned by a letter from their favorite cousin or hunting buddy, came across horrible supernatural events and the survivors emerged shaken but ready to go to the next, unrelated scenario. Indeed, the idea of serial characters moving through a series of episodes has always been the standard setup for horror RPGs! This means Monster of the Week, the game, has a very difficult remit. It has to convince you that it actually brings something different to the table than Literally All The Other Horror RPGs Out There, because this subgenre has been ours longer than it has been anyone else's. We got here first. Buffy's the latecomer.
So, taking that very careful question, what does Monster of the Week bring to the table, there's several elements that combine both to make it an extremely good game in certain circumstances and a very boring one in others.
First, it does a great job of connecting the characters to each other, and using those relationships as the basis for the world. You are giong to be playing episodes of a show that is in its third season. Stuff has happened before. Nobody is going to be "but vampires don't exist!", the most boring thing ever to appear in monster of the week properties. So from a player perspective, it does a good job of bringing you into the dynamic of these kinds of properties. Nobody is going to be lost on the sidelines of a Monster of the Week game.
Second, it does a good job of funnelizing play - meaning that there is always a mechanical way forward. You are never stuck going "well, these werewolves are immune to silver, so NOW what do we do?" There's a simple, basic set of moves (this is a quasi-Powered By The Apocalypse game) that will always provoke you (or send you tumbling) forward through the plot of the scenario. You ascertain the nature of the threat, encounter it once or twice, learn its weakness, and defeat it.
What this means is that for one-shots and for brief campaigns - say, five or six sessions - Monster of the Week is ideal. But these same advantages begin to wear thin as the formula begins to show through. From a GM perspective, there's so little mechanical variation in your options for designing monsters, and none at all for responding to player character actions, that after you do 3-4 episodes, you've literally done everything you're going to ever do in the game. At least the players have their relationships to leap back onto, and a set of moves they can get themselves tangled up in; your options are much more constrained. Compare this to the role of the GM in Apocalypse World, where complicating the situation by introducing a new threat is as simple as coming up with something and saying it happens. The reification of the monster's weakness into a game mechanical token which must be delivered when and only when the players strike one of the moves that generate it means that a lot of the creativity of the GM side is just not there. (Compare, say, to Call of Cthulhu, where every player has 70-odd skills and is clambering all over your monster asking you what happens when they do something involving Botany.)
So that's that - and that was my experience with it. When I ran it once, it sang. When I ran 2-3 sessions of it, it was incredible. But at around session 6 I felt that, as a GM, I'd seen all it could do, and the prospect of more just seemed entirely too dreary. So in that respect, Monster of the Week fails to rise above the typical horror RPG, and, like most of the cultural content it is perching atop of, can't rise to the heights of Buffy-at-its-best. But surely it's better than Supernatural-at-its-worst. And the exceptional, fast-moving quality of the game makes it ideal for one-shot and convention play, so I can urge you to play in those social circumstances with an unqualified recommendation. Just keep an eye out for how the game's structure constrains you.
[4 of 5 Stars!]