I have studied the nature of the glitch for this particular device and verified the following fact:

• Glitches are caused by MSX. No doubt on that;
• Glitches occur only when CLOCK signal change its state;
• Glitches occur simultaneously to the change in CLOCK signal.

then I have added another facts:

• CLOCK signal triggers INT0 on AVR;
• PULSE signals  either real or glitches triggers Pin Change Interrupt on AVR;

Then just as I was considering the last fact.....

• External Interrupts have priority over Pin Change Interrupts!

The solution slapped me in the face!

"CLEAR PIN CHANGE INTERRUPTS AT THE END OF EXTERNAL INTERRUPT SERVICE"

And that was done...

//
// External Interrupt driven by Clock pin (6)
//
ISR(INT0_vect) {
  // output a new bit 
  if (shiftRegister & (1 << MSBIT)) {
    pinMode(DATA, INPUT_PULLUP);
  } else {
    digitalWrite(DATA, LOW);
    pinMode(DATA, OUTPUT);
  }
  // pre-shift next bit
  shiftRegister <<= 1;

  GIFR |= (1<<PCIF );   // <- De-glitch in a single instruction!
}

 The result  can be seen below. Glitches still appear but they do not cause any harm !