There's a piece of plastic in the center of my Nomad windshield above the headlight that slides vertically. Dirt builds up between that piece and the windshield and is unsightly. Can I just remove the sliding part? Does it have any real function?
You can remove the 'window' without worrying about the windshield but you'll have to replace it with spacers the same thickness on each side to take its place in the windshield bracket.
On the other hand, you might want to play with it a little because the part does serve a purpose.
First is cosmetic. If you have your shield up most of the way you have a large gap between the top of your headlight and bottom of the shield. Sliding the window down fills that gap. You can dress it up further by adding a strip of cockpit trim (from a hobby shop) to the edge of the window above the headlight.
Second and more important it's an aero aid.
A lot of head buffeting is caused by air flowing around the edges of the windshield then coming back together in the low pressure area behind the shield. By raising or lowering that window (adding more or less air behind the shield) you can actually 'move' the center of the low pressure area and reduce helmet buffeting substantially. It takes some riding and adjusting to find the sweet spot and it'll be different depending where your windshield is adjusted and your height/distance from the shield so there's no magic formula.
Keeping the area between the window and the shield clean can be a challenge but if you take the shield apart once or twice a year while doing your normal cleaning/maintenance it'll stay fairly clean (looking) until water gets between the panes again. You can try making a gasket using a double thickness of plastic wrap (only because it's clear. Sandwich a strip of the wrap between the window and your windshield along the top edge to help keep water out.