OK so here it is, because I'm never going to get to Fargo to look for that shoe, although if I DID I'd find it. (I'm confident like that).
Years ago after two toddlers went missing and drown in a pond near where I live, I invented or developed an idea for finding people or items that are on the ground.
*). This application works perfectly because it doesn't require the victim to do anything. So autistic people, Alzheimer's, dementia, drunk, passed out, knocked unconscious ect...
*). Most searches end at night, but with this application as soon as darkness falls, this is perfect time. You need it to be dark and the darker the better.
*). In the southern states, scorpion hunters and people interested in certain fluorescent gem stones use a very large Ultra violet light. They wait until dark and shine these lights out and these items GLOW in the dark naturally.
*). Our modern clothing and laundry detergents make our clothes and shoes glow the same way.
When I developed this, I had my children go lay in the grass at night while I looked for them with this UV light and it works PERFECTLY. It's actually fairly amazing how well it works.
When you are using your human eye and a flashlight, your brain needs to sort through everything that you are seeing. It's very easy to misinterpret or overlook something. Especially as searchers begin to tire.
But with the UV light, these items absolutely JUMP out at you.
So extrapolate this further: Imagine trying to search for a white shoe? Well it would absolutely be a piece of cake to drive along, or float along in a boat and shine this UV light in the ditches, fields, river, alley, under bushes ect...ect...
These UV spot lights are readily available for purchase at a very reasonable price on the internet.
Take the other shoe, and a scent hound, narrow down your search area. Ask yourself, how far can someone physically throw a shoe? 100 yards? Wait for night and shine that light.