The obvious thing would be to rotate things sideways and display full iPad 1 resolution apps on screen with maybe 33% screen real estate left over for a menu of some type, or a second type of app, or tabs, or just blank space, and then to allow developers to make new iPad 2 apps if they really want.
1362 x 1024 would be feasible with current CPU tech, battery, and 512MB RAM, and would be a nice bump. Since the iPad works well in either orientation, I don't think this would be a big hit at all. They could also go for another non-standard resolution with a border around another dimension if 1362x1024 were not desirable. But, 1024x768 with 1024x594 left over for something novel seems like it wouldn't be the end of the world for ipad 1 apps, and then an easy way to expand to full screen for safari, mail, and any recoded apps.