Does operation under ETOPS rules require additional procedures in flight during the ETOPS segment?
Most of the action for ETOPS flights takes place during planning and dispatch stages- the planning for alternate airports, gathering of weather reports for diversion cases etc. Before ETOPS entry point, the weather reports are updated and checks are made; after that there are no 'special' procedures to be followed during a (normal ETOPS) flight. 

From Airbus ETOPS Guide:


  3- IN-FLIGHT ETOPS PROCEDURES
  
  b) Weather update
  
  − after ETOPS Entry Point:
  
  The crew should continue to update the weather forecasts and reports
  for en-route alternates. 
  
  As for a normal flight, the crew must make every effort to keep
  themselves informed on the weather at the destination and the
  destination alternate.
  
  c) Fuel monitoring
  
  The procedures normally used as per airline policy is also applicable for
  ETOPS.
  
  This is true even for flights where ETOPS fuel planning is the limiting factor.


In case of diversion (say due to an engine failure), the PIC will take a decision like any other flight, though he/she cannot fly beyond the nearest suitable airport.

One way of looking at this is that the main purpose of ETOPS certification is to improve the robustness and reliability of the design and operator to a level that the ETOPS flight could be conducted like any other normal flight in the ETOPS segment.