My Hero Academia's Mirio Togata wasn't one of U.A.'s big three without reason. By working hard on his powerful Permeation Quirk, which has many downsides, Mirio was able to work at a reputable agency, and was well on his way to going pro before being "relieved" of his Quirk. But regardless of whether or not he gets it back, its hidden secrets will remain the same.
Mirio Can't Breathe, See or Hear While Using Permeation
Mirio's Permeation Quirk is not for the faint of heart, as literally everything passes through him. As he revealed in his debut -- Volume 14 of My Hero Academia -- light and air also pass through him, effectively rendering him blind, deaf and mute instantaneously, though surprisingly not invisible as one would assume, with light passing through him.
Not only must this be a terrifying thing to experience suddenly, but it also means that for a precious few seconds, he loses all perception of the battlefield, meaning the longer he "falls," the more likely the situation and positions of the combatants have changed. This is why the emphasis on "predicting your opponent's moves" at the Nighteye agency allowed him to surpass these limitations and become a competent fighter.
Furthermore, his Quirk is so absolute that an entirely new material needed to be created using samples of his hair in order to make a hero costume that could phase with him. Why his everyday clothes aren't made of this, we don't know. Nor do we know at what point the food he consumes gets to be considered "part of his body" by his Quirk. Honestly, we're surprised that he doesn't lose his lunch every time he phases!
When Mirio Activates Permeation, Momentum No Longer Applies (But Gravity Does)
Going underground to avoid attacks and hide positional changes from his opponents is a key component of Mirio's battle technique, and making it appear like he can "warp" around the battlefield certainly has its advantages. As Mirio himself explains in Chapter #123, two objects cannot occupy the same space at the same time, resulting in him being forcefully ejected, something he has a small amount of control over by changing his body position underground. But the real question is -- why is he underground in the first place?
When he activates his Quirk, no matter what he's doing, he goes straight down, and Mirio himself claims to still have mass, which is affected by gravity. With gravity being the only force that affects Mirio when he uses his abilities, it's easy to see how he could quickly find himself in the Earth's core. Fortunately, falling takes a while, even without air resistance. So, Mirio usually has some time to reposition himself and release his Quirk, popping up where he intended, rather than halfway across the globe. It also opens up some interesting possible interactions with Uraraka, whose Quirk would remove even gravity's effects.
The Strongest Part of Mirio's Quirk Is His Level Of Control
With all the disadvantages that his Quirk gives him, Mirio has to be very smart about how he uses it. He needs his mouth or nose to be tangible so he can breathe; needs to be aware of what parts are tangible and which aren't to make sure he doesn't get stuck in a wall; split in two or start spontaneously falling, and, when not wearing his hero suit, he also has to be aware of exactly which items of clothing are falling through him.
Couple this with his prediction training at Nighteye's Agency, and Mirio soon becomes a force to be reckoned with; basically untouchable on the field of battle. He can "phase out" all but the soles of his feet to continue running, or have just his knuckles take the impact of his punch as he phases through his opponent's physical defenses.
But, though Mirio is absolutely great in a fight, rescue work gets a little harder. After all...
His Permeation Will Only Ever Apply to Him
Unlike other wall-phasing characters, like Danny Phantom, Mirio can't take anyone with him into his permeated state. Even by grabbing onto them while solid, then activating his Quirk. This is a huge issue in hostage and rescue situations, as while the villains can't touch Mirio, they most certainly can touch the innocent bystanders.
Doing so forces Mirio to make use of his muscles and take those blows, putting himself in harm's way rather than letting someone get hurt. Even without a villain to make the situation worse, Mirio's inability to make other people permeable means that while he can locate the injury in a building, he can't take first aid supplies with him to tend to them there, and unless he carries them, he can't bring them out to receive medical attention at the scene.
This helplessness, despite his powerful Quirk, would likely make him gnash his teeth in frustration, but he certainly isn't one to ever give up. While he can't phase people out of danger, we know he'd both fight to defend them till the end, or relay coordinates to rescue teams, and then go back to the injured to make them laugh and smile while he clears the path.
Mirio Struggled to Master Permeation For Longer Than Most
Mirio's Permeation is a hereditary Quirk, having been passed down to him from his father, who understood how difficult and potentially dangerous their ability was -- to the point that he even tried (briefly) to dissuade Mirio from following the path of a hero, a path Mirio's father had given up on himself. But seeing his son's determination, he promised to support him all the way.
And so, Mirio's long journey towards control began, first learning how to activate and deactivate his Quirk safely, then trying to intentionally phase through things. By middle school, he was able to activate his Quirk on specific body parts, rather than full-bodied. He was still struggling to control his Quirk through his second year at U.A., where Deku watched him leave a rather... interesting impression on the Sports Festival.
Of course, we're referring to the fact that the sports festival is done in gym clothes rather than hero costumes, meaning that, uh, Mirio was constantly losing his. It wasn't until he was scouted by Sir Nighteye that Mirio was finally able to utilize the full potential of his Quirk and become the hero we know him as today.