As the title states, the eMac has a clear section at the back of it's housing that forms a grill for the fan inside. This seems to be pretty good at catching dust that's impossible to get at simply by removing and washing the housing, is there a way to remove this part so I can actually get it clean?
There are take apart guides a Google search away (including the official Apple Service Source one), but from what I can see, you remove the two front feet with a #2 Phillips screwdriver while the eMac is face down on an ESD mat, then use a 2.5mm hex screwdriver to remove the three large-headed screws around the access plate on the bottom, then the six screws around the screen end of the rear housing (two each top, left and right).
Gently lift approx 5cm only so you can (gently) disconnect the power button. The rear housing should then be able to lift off completely. I highly recommend reviewing the take apart guides befor starting!
I've not found instructions for removing the grill/vent from the rear housing, but at least you should be able to clean it when the rear housing is removed without fear of wrecking the internals.