Nichirin Swords Are Inherently Particular to Every Demon Slayer
Nichirin swords are a fictional type of katana that's been especially crafted to destroy demons. They're fabricated with two legendary components: Scarlet Crimson Iron Sand and Scarlet Ore, which are said to absorb and be infused with sunlight, hence their demon-slaying properties. It is said that the color of the blade changes when a demon slayer first wields the weapon, and this color is associated with their breathing technique. Inosuke's Nichirin Swords are indigo-gray, unique to his Beast Breathing technique, of which he is the only known user.
The nichirin swords are zealously crafted at the swordsmith's village, a location kept secret throughout the series. In episode 25 it's seen, though, that Inosuke does not receive his swords with the serrated finish, and in fact, it's him who forges the saw teeth with a stone, much to Haganezuka's rage. Along with his boar head, and him going around topless, there is no doubt that Inosuke has got the most peculiar appearance out of all the Demon Slayers.
Why Do Inosuke’s Nichirin Swords Have a Serrated Blade?
The reason why Inosuke's blades are serrated is both logical, in terms of Character Design, and coherent, in relation to his personality and lore. Serrated blades are aggressive-looking, which is connected to Inosuke's general "feral" attitude. Just like all the girls in the Butterfly Mansion wear butterfly-themed hair accessories to reinforce the way they evoke, the serrated swords are complementary to his persona. It's not only that, they also lack a proper handle. They are only wrapped in some bandages so that Inosuke can manipulate them without cutting himself.
In the Official Fanbook: Demon Slayer Corps Records, Koyoharu Gotouge stated that Inosuke has a preference for these menacing-looking blades because they also resemble a threatening animal's jaw. A blade with these chainsaw-esque teeth will also deal more damage, something that can be appreciated in real life when trying to cut a steak with a serrated knife versus a regular one. A sword of this kind would require more maintenance, but surely Inosuke is very capable of doing this if he makes the swords like that himself in the first place.
The Importance of Swords Is Pushed Throughout the Series; Especially In How They Define Certain Characters
Thanks to their colorful designs and personalities, it's very easy to tell characters apart in Demon Slayer. When it comes to the Demon Slayer Corps, it seems like they're given a lot of freedom in terms of customizing their attire and weapons. In Inosuke's case, his untamed personality might not leave them another choice. He not only barely wears the uniform, but also wields two Nichirin Swords that are serrated.
Inosuke is not the only one with a notably distinct weapon. The Love Pillar, Mitsuki Kanroji has a whip-like nichirin sword, if it can even be called a sword, but regardless, it is still a regular, even blade. The same applies to other members of the Demon Slayer Corps who have a weapon different from a regular-looking sword: the blades are still flat and even.