It is in recognition of this fact that Metro-Goldwyn-Mayer has assumed a rare responsibility and acted with remarkable dispatch. In "The Beginning Or The End", it is bringing to the screen the important, timely story of the atom bomb. And despite the immensity of the undertaking, filming of the picture's final scene was announced less than one year following the date of Hiroshima's devastation.   In the intervening period, Hollywood met and solved a staggering miscellany of problems — all bound to arise when dealing with America's "top secret".   Not the least serious obstacle was the obtaining of all approval from dozens of living personalities to be portrayed in the picture, including the President of the United States, Harry S. Truman. When a completed screenplay was achieved, the White House joined the War Department in officially approving it.   Paving the way for one of the rare instances that a living President has been portrayed on the screen, consent was achieved to depict Mr. Truman as he made his historical decision to use the atom bomb against Japan.   Without such official approval and without the government cooperation tendered Hollywood throughout, the true story of the atom bomb never could have been filmed.