Let me see if I understand the "surface" of the "Filtering Out" process: untrained, the MC can't control his power, which somehow makes him show up on the Dark World's radar but doesn't let him actually do anything significant. No "summon lunch" spells, but would he be able to do unsophisticated minor stuff like shoving or yanking relatively low-mass objects (like pencils or pieces of paper)? Anyway, the MC's magic itself doesn't do much of anything but give the Dark World's agents something to target with their own spells. Standard procedure is to slowly erase the target's emotional bonds with the Mundane World; first by preventing him from making any new friends, then making it harder and harder for him to maintain any previously existing relationships. Meanwhile, the paper trail valued so highly by the Mundane World gets erased, lost, misfiled or generally removed, making it that much harder for the MC to get anything official done. He's not old enough to worry about a driver's license, but I suspect that his cell phone bill keeps getting misplaced, and his Internet accounts keep getting erased, and so on.
Not quite. People are filtered out when their magical power has reached the point of no return, when they are no longer considered "Normal" by any means. This is supposed to tie into a theme in the story of the Magical World being clear cut black and white and the MC not seeing it that way.
You are filtered out when one of 2 things happen to change you status and there isn't a lot of gray area to the Wizards involved.
The first way is when your magical skill and use causes "ripples on the pond" magically speaking. Not everyone with magical power is filtered because magic in the Light World of Mundanes is limited(It's being redirected mostly). So, there are a fair number of minor talents in the real world, but their spoonbending talents let's say aren't strong enough to merit anything but a trip to the funny farm.
When a magic user becomes aware of magic, it's like a Deaf person learning to hear for the first time, everything is loud and overwhelming. The first use of magic is the typical fair in a story like this, the X-Men-esque "Holy Crap, what did you just do?" moment. This moment or series of moments gets picked up on the radar at the point when you ain't normal no more which also the point at which the things that go bump think you are tasty.
The second way is when you are identified early. Magic users from the Dark World of things actually come to the Light world for a variety of especially political reasons but one is to identify Magic-Users early and speed the process up.
Also, Magic use is something you can catch onto pretty quick, albeit in an unsophisicated way. "Summon Lunch" spells not withstanding, there was probably a lot of weird stuff happening around the MC prior to his filtering, but he passed it off as happenstance til he blew something up with a makeshift Fireball.
The reason people are filtered in the first place is to keep magic in check and its users away from persecution and believe it or not, enslavement.
Is there a point at which the Mundane World essentially acts like it can't see him?
Yes, there is a point like that.
What happens when the Dark World predators you mention show up and he can't even get the other people in the room to react to the threats?
What do you think happens? He runs like hell until he figures out how to blast them.
People in the room react via Occam's Razor and The greek Titaness of Memory hand-waving it away.
These are good ideas. So, your MC will come into the Dark World with a portion of his memories irretrievably gone? Where will his pop-culture references come from? But seriously, how does that allow the two worlds to be connected?
When someone is filtered, not every memory is wiped. If that were the case, new Wizards wouldn't know how to tie their own shoes.
The MC retains his knowledge and skills, but forgets the context of them. Example, he'll remember a scene from a movie, but he won't remember the context in which he saw it. Plus, the MC makes a bargain to retain some of his memories(which subsequently tanks his exam scores) and the MC uses mnemonic devices to remember his past.
He also keeps a journal, which he reviews every night.
Going from Light to Dark Worlds and back is like crossing the Berlin Wall. Must have a passport or jump the fence.