Richard Burton’s legacy is one of contradictions. He is both a towering figure of 20th-century popular culture and a bright, brief candle whose peers made indelible marks on the 21st, too. He managed to achieve success as both a classical stage actor and marquee-name movie star at a time when slippage between those worlds was at a minimum. He was nominated for an Oscar seven times, but never won. His relationship with Elizabeth Taylor—with whom he co-starred in many films and stage productions, most famously Who’s Afraid of Virginia Woolf?—is remembered as an epic love story despite their twice divorcing. He described himself as a socialist, or indeed a communist, but moved to Switzerland to avoid paying taxes, wryly commenting, “I believe that everyone should pay them—except actors.” Famously an alcoholic, he claimed to drink to stave off the deadness of being offstage. Sometimes his alcoholism was functional; other times he was reportedly so drunk, like while filming The Klansman (1974), that he had to shoot all his scenes sitting or lying down. By his forties, he had become frail and weak. By 58, he was dead.

Mr. Burton is not about any of this.

Based on the early life of actor Richard Burton and released earlier this year to little notice, the biopic Mr. Burton is a bit like a pointillist painting. At a distance, it makes one picture, but up close, the dots of color disaggregate, unsettling our assumptions about the whole.