According to Japanese Mac blog MacOtakara, the next-gen iPad will have a flatter backside and smaller bezel compared to the original iPad. The "iPad 2" will also have a larger "wide-ranged speaker" located behind a mesh speaker grille.
MacOtakara notes that their Chinese source has told them the next iPad will be three millimeters smaller than the original, but the display will stay the same size. That means the bezel surrounding the iPad's display should shrink substantially. The rear case has been flattened to be more like an iPod touch, which should make it easier to lay on a flat surface. Though I didn't mention either of those things in my list of things I'd like to see in the iPad 2, a smaller bezel and flatter rear case would definitely improve the iPad's design, and if this image from MacOtakara accurately represents the revamped speaker, we can expect much better sound out of the next iPad as well.
MacOtakara's source claims production of the iPad 2 has already begun, with orders scheduled to begin shipping to Apple by mid to late January. This aligns well with an earlier iPad 2 shipping date rumor from Digitimes. MacOtakara also notes that, while "unreliable information," the next iPad may have both front- and rear-facing cameras, with the rear-facing camera having the same resolution as the iPhone 4.