Ok, so the signal is a bit messy. Have you tried to see if the firmware in the PIC will actually recognize it as a character? Something like turn on an LED with an $aa recevied, turn it off with a $55 received, or something simple.

I seem to remember doing some probing myself way back when (albeit with a Tek 2246A, nothing near as nice as yours!)...and it seems to me the output was a bit sloppy there too, but it worked just fine.
Also, the other issue might be the fact that you're running at 9600. Try slowing to 2400 and see if that cleans it up a bit, if not, try 19200 or higher.

Just curious...are you sure you're actually transmitting at 9600? The 'scope picture says 250ms at the bottom. Are you sure the OSC define is set right? Oscillator is running at the right speed at both ends? It sorta looks to me like your data is coming out about 8-10 times to slow. I could be reading something wrong though...

JDG