How common are regulations limiting when the FO can be PF? I was reading that in India regulators have specified certain airports at which the FO is not allowed to take off or land.    


  The Pilot-in-Command shall not authorise a Co-pilot to effect supervised take-off or landing when TODA/LDA is  marginal. A margin of at least 1000 feet must be ensured.  Critical airfields,  [Mangalore, Port Blair, Leh, Agartala, Lengpui, Shimla &amp; Kullu airports]  are specifically excluded for supervised take off and landing.  


As a matter of fact they have several limits in place where 'supervised takeoffs and landings' are not allowed and the PIC must fly the plane.  

In this unique to India or are limits on FO's common?
All the airports listed in the AIC are quite tricky to takeoff/land in. For example, the Lengpui airport runway is a classic example of tabletop runway.



Source: www.misual.com

The Leh runway is surrounded by steep hills.



Source: geolocation.ws

The kullu airport runway has a river in both its ends.



Source: www.airportsindia.org.in

This is the reason for these restrictions. I'm not aware of any such regulatory restrictions in case of other countries. However, the operating airlines can have their own rules about (Category C) airports.