“The Deer Hunter” should not have been as good as it is. The production was beset by major problems from the start, including bitter infighting, a terminally ill cast member, a runaway budget, and a narcissistic director who may not have been cut out for the job. But it hardly mattered. The Vietnam War drama won five Oscars at the 1979 Academy Awards, and is still widely regarded as one of the greatest films of the 20th century.