I had this problem once (actually, it too was an RS232 app).  Try running
some additional ground wires here and there and back to the main ground
point.  That did it for me.

-Vincent

 > Thanks very much to everyone who helped me
with this. >
> I got things *kinda* working (transmit only for now) running at 4.5v,
> cts<->rts and dsr<->dtr, and with 200 Ohms from the pic xmit pin to the
> rs-232 Rx line. Current unsolved mystery is why  it only works reliably with
> the scope's ground clip attached to my circuit ground (with scope probe
> unattached.)...
>
> Cheers,
> Dan
>