Strange flickering In 2.5D rendering

I’m messing around with a 2.5D effect–I’ve set up a four-layer scene with alpha channels on flats and I’m animating the camera through them for parallax. The problem is the last layer keeps getting a weird diagonal flicker of disappearing pixels across it, no matter what I do. I disabled MIP mapping and specularity based on some ideas I found on the web, but no go. It doesn’t seem related to ray bounces, either.

Earlier, I was getting a black bar across the renders from the top right to the bottom left, but that was either a video encoding artifact or something even weirder because it went away after redoing the image mapping and switching from AVI to MPEG output. I’m rendering as frames now and still getting the effect. Any ideas? I’m uploading frames 98 and 107 to show the effect. The frames in between are OK. Those background trees should be visible and not invisible in a diagonal band.

For comparison, here’s the frame before, number 106.

I seem to have solved it. It turns out to have been two things–setting the camera clipping to the lowest possible setting and subdividing the planes. Oddly, I’d tried subdividing the planes before, but only subdivided them twice. Three subdivisions and the clipping plane seems to have done it. Frustrating!