A great movie with some improbabilities
Overall, I consider it a great movie. It has suspense, cinematography, all. Fully recommended!
To make it short, and hopefully not spoilers, two items struck me as unbelievable. Firstly, the bullets in the body couldn't be traced back to the rifle found on the roof terrace, rendering the whole official story almost impossible, even though the commission had to find a solution without conspiracy. This fact is just too obvious. Likewise the suicide. Even by placing the pistol next to the 'assassin', nothing would point into that direction: distance of bullet entering, angle of bullet entering the body (the viewer has seen both), lack of smoke and powder on the hand, and so forth.
And, though not that important, by fabricating some false witnesses, the chance would be higher that the matter be given away. Even if you paid the bespectacled bold chap 1000, he could always start talking. And if you can arrange everything that phantastic, you wouldn't have the live-TV truck obscure the 'witness'.