Is there a way for pilots to report difficulties and challenges experienced during a flight, to the next flight crew? My question is reflected in the title - is there an official, international system for commercial pilots to report difficulties and challenges faced during a flight to the next and future crew? Ideally, such a system should also require the next crew to review recent entries into it. Does something like it exist and if so, how strictly is it followed?
"Difficulties" are hard to quantify. And it's questionable whether a difficulty experienced by one flight is even relevant to the next. Many difficulties are transient in nature (eg: weather, crew, cargo loading).

However, there is what is known as an Acceptable Defered Defect:


  An identified aircraft defect which has been assessed as being within the requirements of the Minimum Equipment List (MEL) or Configuration Deviation List and has had rectification deferred within a specified limit. Also referred to as a CFD (Carried Forward Defect)


This is used to notify future aircrew of a specific aircraft of any defects which, although does not require the aircraft to be removed from service, may be relevant to its operation. 

Pilots absolutely check this before every flight.