It can be difficult to tell if your DSP code is taking longer to run than the available clock cycles between samples.  The DSP56364 ignores a second ESAI interrupt if it is still processing the first one, causing it to drop samples.  In my case, the effect pretty much worked, but the missed samples added a small high-frequency signal.

I added the following code to the beginning of the receive exception interrupt (esai_rxe_isr) to detect receive overruns.  It uses one of the debug memory locations as a counter, so it's unobtrusive.  The actual number of overruns isn't important - just the fact that the number is changing.

     ; Check for receive overrun
     move     x:M_SAISR,a
     jclr     #7,a,_no_receive_overrun
     move     x:Debug_Read_from_DSP_4,a0
     inc     a
     nop
     move     a0,x:Debug_Read_from_DSP_4
_no_receive_overrun