American diplomats in Panama are facing a variety of real and potential problems brought on by the Reagan administration's decision to have no dealings with that country's military-dominated government, U.S. officials say. In addition, harassment of American servicemen is on the increase, prompting U.S. military officials to take precautionary measures. Panamanian officials respond that troublemakers among U.S. military personnel pose daily headaches for Panamanian authorities. The State Department's constraints on U.S. envoys are such that they are prohibited from carrying out even simple tasks, such as renewing their license plates or their driver's licenses. As a result, many diplomats have been forced to rent cars rather than run the risk of driving with expired plates. Some make their rounds with expired driver's licenses, worried what local authorities might do if they catch them in a traffic violation or an accident, the officials said. The diplomats lack the documents entitling them to diplomatic immunity. Thus, they are subject to imprisonment if found guilty of a legal infraction. According to U.S. officials, there is concern that agents of Panamanian leader Gen. Manuel Antonio Noriega might stage an ``accident'' in which an American diplomat might be subject to prosecution. The diplomats have been in this unusual position since last February, when the Reagan administration refused to recognize the de facto government that took office after the ouster of President Eric Arturo Delvalle. Delvalle was deposed after his abortive attempt to fire Noriega, commander of Panama's Defense Forces. Noriega has been indicted on drug smuggling charges by two Florida grand juries. By withholding recognition from the Noriega-led government which assumed power after Delvalle's ouster, the administration hoped to force its ouster and to lay the groundwork for the restoration of democratic rule. There were confident predictions in Washington six months ago that Noriega soon would be forced to surrender power but, with key elements of the Defense Forces supporting him, he has been able to maintain his position despite widespread popular opposition. Meanwhile, U.S. diplomats and others in Panama have been forced to make difficult adjustments. There have been increased incidents of harassment of American servicemen but U.S. officials do not believe the actions represent deliberate harassment by the Panamanian government. Earlier this week, Panama's Defense Forces issued a statement denying a published report that American servicemen are being singled out for harassment. The statement said U.S. troops cause daily problems for Panamanian authorities, including fights, mistreatment of women, venereal disease, shooting in public places and refusing to pay bar and restaurant tabs. According to U.S. officials, the most serious incident involved the Panamanian wife of an American serviceman. The officials said she was raped by two Panamanians who were wearing Defense Force uniforms. There also have been reports of beatings and abductions of U.S. military personnel. Cynthia Farrell, a spokeswoman for the U.S. Embassy, said American residents of Panama, including businessmen and embassy personnel, have reported no increase in harassment. But an official at the U.S. Southern Command in Panama, who spoke on condition of anonymity, said 240 cases of harassment of U.S. servicemen had been reported between February and August of this year. In response, the Pentagon has been sending some servicemen back to the United States or moving them to safer locations in Panama. The Southern Command official said an increasing number of Panamanian policemen have been attempting to bribe U.S. servicemen stopped for traffic violations. But he noted that the police have not been getting paid regularly because the government has been short of cash since the start of the year. In another example of harassment, the Defense Forces recently refused to allow U.S. military personnel to pick up mail at Panama's international airport for three days, the official said.