For a crystal oscillator circuit, what effect would a series resistor have on the inverter input?
The questions are about the 280-Ohm resistor on input. The picture clearly states that it is "ESD pad", and the value "280" likely represents the lump model for this pad cell.


  
  Does this "resistor" have any effect on the transconductance (gain margin) of the circuit design?
  


Yes, the resistor generally reduces overall gain of the amplifier (due to small parasitic cap on the internal inverter input), but the loss of gain is likely compensated in the inverter design.


  
  Is it likely to introduce any other effects that needs to get taken into account in the design?
  


Not really, see above.


  
  Would there ever be a reason to deliberately design in a resistor connected the inverter input?
  


This is just a model for ESD protection on the pin. Since the actual internal input impedance is likely in mega-Ohm range, the 280-Ohm shouldn't have much of impact. Even if the inverter input has 1 pF parasitic capacitance, the RC cut-off will be in ~3 Ghz area, or well outside the typical working frequency of 20-40 MHz

Therefore, the input resistor should be of no concern for the overall design.