A ONE-TIME Shanghai film actress, Mrs. Mao Tse-tung has put on quite a show in the Peking courtroom where she is being tried for treason and the like. She has sassed the court, stuck to her old political guns, attacked those who put her in the dock and dared the government to hand down the death sentence that would seem to be indicated by Chinese law. The court -- or, to be more precise, the government -- has been sitting on the case for more than two weeks, seemingly unable to decide whether to execute and make a martyr of her or to let her live on, with all the uncertainties that could entail.

But perhaps it is bourgeois of us to salute the Great Helmsman's widow simply for the vigor of her defense against what are patently political charges flowing from the ascension of a new leadership clique. For she is not merely a gutsy and, admittedly, disruptive woman trying to either go free or go into history. She is a political person struggling to revive her and her late husband's political cause. When you look at her show trial in this context, something other than her personal performance stands out. She is being given a forum on China's official television for her counterattack. This could hardly happen if she did not have friends in high places still.

No doubt it is extreme to say that China's current leader, Deng Xiaoping, has failed in his effort to use the "Gang of Four" trial to discredit the Mao way of modernizing by perpetual revolution and to strenthen his own policy of modernizing by selected reform. But certainly Mr. Deng has fallen short. Tough decisions -- some experts call them the most crucial since the Communist Party took power in 1949 - are on Peking's calendar this year. They involve the party's ideology, membership and governing policies. The unanswered question is whether Mr. Deng will be better placed to tackle them after the trial or whether, in attacking the "Gang of Four" head-on, he is playing Mrs. Mao's game.

As far as the United States is concerned, this is one of those situations where the stakes -- conceivably the whole foreign-policy orientation of the People's Republic -- are of surpassing importance. Yet for the United States to try to poke its nose in, however discreetly, would be intolerably risky. This is why it is disconcerting to see President-elect Reagan still maintaining a certain ambiguity about the "normalization" of relations that President Carter negotiated with China. Few charges could be more telling in an internal Chinese power struggle than the allegation that one side had yielded unwisely on Taiwan.