One place on the globe where the news looks dandy these days is China. Mme. Mao and her radical pals in the Gang of Four have been tried and convicted. Their sometime ally and Mao's successor as party chairman, Hua Guofeng, has suffered a fall. So it figures that the pragmatic, relatively pro-American leader, Vice Premier Deng Xiaoping, is firmly in the saddle.

Only that isn't the way the professional China experts see it. In their view, Deng has scored short-term gains by taking long-term risks. Even now he is said to be passing through a messy political crisis that requires delicate handling of China by the United States.

The trial of Mme. Mao, or Jiang Qing, as she calls herself, wallowed in disorder. It started a couple of weeks behind schedule. It stopped for several days without explanation. Instead of the docile confession of guilt required by good form, Jian denounced the present leadership.

In the process, Mme. Mao raised a crop of politically embarassing subjects. She declared persuasively that all her actions were done at the bidding of Mao himself. She tied Hua Guofeng to the Gang of Four and to overt opposition to Vice Premier Deng. She even questioned Hua's claim to have been anointed party chairman by Mao with the famous comment, "With you in charge, I am at ease." As Mme, Mao told the story, what her husband really said was: "With you in charge I am at ease. And if you have any questions, check with Jiang Wing."

Those charges evidently forced Deng to move more quickly than he had planned against Chairman Hua. The move came in an informal work conference of the Party Central Committee held from Dec. 16 to Dec. 25 -- that is, while the trial was still on.

The meeting apparently decided to eliminate the post of party chairman, which was created for Mao and passed on to Hua. In addition, Deng replaced Hua in the other key position he inherited from Mao -- chairman of the Military Affairs Committee.

Though Deng clearly won these encounters, the victory did not come cheap. The idols of Chinese communism -- not only Mao, but also Stalin and Lenin and Marx -- have been toppled. With their reputations in semi-disgrace, a sharp debate has been opened with the party.

Among other questions now being openly debated are these: whether a multiparty system is better than a one-party system; where Mao went wrong; whether the October Revolution that brought the Bolsheviks to power in Russia was fascist or socialist in character.

Lack of discipline has spilled over into every other activity. Reports of local elections show Communists regularly losing to non-Communist candidates. lExamples of malingering on jobs in both the countryside and in factories and offices are commonplace. Unwillingness to work hard is being blamed, among other things for failure to meet the targets laid down in the program for modernizing China.

These Chinese shadows have evidently had a particularly bad effect on the military. Many top soldiers were close to Mao as comrades in arms. They were also wooed assiduously by Hua Guofeng last year.

Deng addressed himself to these problems in a secret speech to the party work conference on Dec. 25. According to one account that has reached Washington, he attached "certain current ideas that everything will be fine so long as stress is laid on profit." He is also said to have called for disciplinary action against "counterrevolutionaries, criminals and lawbreakers so as to consolidate the dictatorship of the proletariat."

So far, no clear opposition to Deng has emerged. But the feeling here is that there are many potential opponents -- and on all sides. Deng, it is believed, has to play for time. Thus a scheduled meeting of a leading state organ -- the Standing Committee of the National People's Congress -- has been postponed.

What seems clear is that at this juncture Deng doesn't need any more trouble. Which is where the United States enters the picture. So far, in naming officials and in the inauguration ceremonies, the Reagan administration has avoided the tilt toward Taiwan that emerged in the campaign. But any waffling on that score, any concessions to the right-wingers in Congress, would make new difficulties for Deng and raise the risk that China would become less helpful to this country in he common strategic task of blocking Soviet expansion.