When Joseph Losey gets his hands on the right material he can do wonders with it. This doesn't seem to have been the right material, or maybe Losey was just impatient with Burton's boozing or something.
First, don't expect a biopic of Leon Trotsky, the stormy petrel of revolution. The title describes the assassination of Trotsky. He's a professorial sort, exiled to Mexico City after Stalin took over and betrayed Lenin's principles by playing footsies with Wall Street. It often happens with extremist ideologies that they split up, because everyone wants to be purer than the next guy. At that, Trotsky was lucky to get out alive. Stalin had ANYONE who represented a threat to his power murdered. Stalin went about, doing bad.
It's an unpleasant movie. We have to sit through a bullfight and learn why movies usually don't show us the final coup, after which the bull drags himself around vomiting blood until he flops down, while the crowd cheers. I know -- the bravery and grace of the matador and all that, but why don't they just let the bull go? Sometimes there is a thin line between beauty and baseness. I understand why the scene was included. The matador does to the bull what Alan Resnais does to Burton, more or less. And instead of dying a neat Hollywood death, Burton staggers up from his chair, a hole in his skull, stares at Resnais and shrieks bloody murder.
There are long periods in which we watch Mexicans doing nothing in particular. And the scenes can be confusing. It's not always easy to tell what's going on. The musical score appears to have been made by a thousand chirping electronic crickets.
Lots of talent and momentous intentions gone awry.