I recently replaced the air filter myself on my 420 SEL.
Forgive my ignorance, but I will show it in the following questions:

What is that smaller filter insert on the side of the air chamber?
What does it do, and what is the hose for leading from it?

Finally, what problems might be encountered if that smaller filter unit is worn/dirty, or the hose leading from it is loose?

The smaller filter on the outer edge of the air filter housing (looks like the working end of a small push broom) filters the air going into that hose that comes out of the air filter and goes down to the secondary air pump (or smog pump). I am still not sure how this pump works, but generally it only works during start up and extra air is pumped into the exhaust making it easier for the cat converter to process it. I could be wrong about it function, but that is where that hose goes, and I can see the need to filter that air, especially if the air passing through it goes to the cat converter. I change that filter when I change the big round one. If the hose is loose you should replace it, it is pretty cheap. Mostly it has to do with emmissions control.

'smog'filter(?)
 

Thanks, Jason.

Incidentally, when I tightened this hose connection from the air box, an exhaust smell I had been noticing-particularly with my windows open - largely disappeared. Does this logically follow your explanation that it is a smog-pump connector?

Yes, When mine went the metal connector where the hose goes into the engine block had corroded and separated. I also had an exhaust smell in the car until I fixed it.