I have a special problem with respect to valve that are used in offshore oil and gas industry. A perticular manufacturer supply us valves complying all the testing and specification requirement. But it is observed the all those valves start passing within a very short span of time. Therefore, I would like to know what are the things that is required to review during finalisation of purchase specification.

It shall be of extreem help if you kindly help me in this regards.

Sounds like the valves passed factory leak tests, but quickly leaked once put into service.  If so, the problem is not that something was missed during finalization of the purchase.  The problem is that the proper effort was not made before purchasing.

Keep in mind that the factory tests are not intended to prove the valve is going to work in a particular application.  They are a quality check that verifies the valve was manufactured and assembled correctly.  Work needs to be done upfront, before purchasing to verify the valve is the best choice and will work in the application.  You can request special testing that may duplicate the service conditions (to the best that is practically possible), and learn if the valve will work.  But then it is far too late and a waste of everyones time if it doesn't pass this test.  It is also much more expensive to do special tests.  Just do the work upfront before purchasing.

ANSI B16.104 is obsolete and withdrawn.  See FCI 70-2 for Control Valve Seat Leakage.  This is much greater leakage than required by API STD 598.

It is common for new valves to meet the zero bubble requirement in API STD 598 when new.  Sand was already mentioned.  The nasty rusty hydrostatic testing fluid is often left in the lines for a prolonged period leaving scale and such in the seats.  Such practices cause the valves to leak even during the initial startup.

Some attempts to fix the problem include adjusting the limit stops to get a fresh piece of the seat into service in addition to the lubrication tricks.One trick not mentioned is to use a plug valve.  
Nonlubricated valves have a (usually) PTFE sleeve for sealing. The plug has a 2 degree taper.  If you catch 'em leaking, there is an adjustment to drive the plug farther into the taper, restoring the shutoff.  Nonlubricated plug valves are available thru ASME class 600, Lubricated plug valves are available for higher pressures.  Ball valves are hard to turn, but comparatively, plug valves are HARD to turn.  Bring a long, long, cheater bar.