Wow, what a great community; a lot of responses in a short time!
Toontoonz: I can't tell how you put the image together, but I have each jaw on a different layer, and I stretched them to make the fringe more visible. This problem first showed up in a "This Land" JibJab style cartoon that we're working on. All the PNG body parts have the fringe. My Moho file is 720X540, and the pic I posted is part of a screen cap of a rendered frame. The jaw is 112X78, and I've seen the fringe in all resolutions I've tested.
7feet: I am using a clear background when I create it; the famous Photoshop little gray checkerboard background. The PNG, when loaded into Photoshop or Microsoft Photo Editor, shows the same clear background. It looks clean in Moho as well, until I render.
LostMarble: I’ve tried Photoshop 5 and Photoshop CS to make the PNG. There is no pre-multiplied alpha channel fringe. There is always a 1-pixel-wide circle of a single color surrounding the images when Moho renders it. I am using villagephoto.com to upload the images, and they won’t accept a PNG file, so I don’t know how to post it. I have emailed the file to you instead.
How to recreate the PNG matte line problem:
In Photoshop, make a new 100X100 RGB color file with transparent contents. Make a light gray foreground color (I chose R 230, G 230, B 230). Use the elliptical marquee to make an oval in the center. Choose edit>fill and use foreground color at 100% opacity in normal mode. Hold down CTRL+SHIFT+ALT+S to Save for Web. Choose PNG-8, Selective, Diffusion, Colors 256, Dither 100%, Matte None, Web Snap 0%. Save it as oval.png. Here’s a screencap of my settings:
In Moho, choose File>New, then in File>Project Settings set the dimensions to 720X540. Choose File>Import>Images and load oval.png. In the Tools window, choose Scale Layer (or press 2), and then scale the layer to about 6 times its size. In the Layers window click the Duplicate Layer icon. In the Tools window choose the Translate Layer tool (or press 1). Move the layer down and to the right so that it overlaps the original layer. It looks fine now, but hold down CTRL-R to render. I get this:

Thanks for the replies; let me know if you can recreate this with your Moho. I have version 5.1 of Moho.