The scope has been done before
PIC18F2550 KS0108 Graphical LCD Oscilloscope. The chip looks similar (in specs) to a Mega32, but a lot of the code is for the LCD. He also has a version that displays in software on a host machine and it's a
lot smaller. (He actually made his version as an HID device hehe) But that's just one example, I've seen others, even CRT PIC based scopes. I will look and see what I can do for a logic probe, but the scope is beyond my skills :/ But it can be done for very cheap. Bringing the display to the computer makes things a lot easier. From the little I dabbled with Processing it also looks like it's very well suited for graphics so that shouldn't be too bad. I actually think it would be quiet quick to assemble. It might not give Mhz range, but 0Hz to ~600Khz is still useful. Specially with the frequency generator (there's some chatter in a thread by CosineK.) which is in that range. Also, afaik using (fast) fournier transform it's possible to obtain full sinusoidal waves.