The Government

The administration made good on its threat to fire controllers who failed to appear for work at the beginning of their first scheduled shift after 11 a.m. yesterday. Dismissal notices went out yesterday afternoon for those who failed to show up for the 3 p.m. shift; morning shift workers have until 7 a.m. today to return or be fired. A White House spokesman says President Reagan remained "solid as a rock" in his decision to fire the controllers. The Union

PATCO officials said its members were holding firm. Hundreds of striking controllers met for solidarity sessions in union halls as Reagan's firing deadline approached and passed. Union President Robert E. Poli said that the controllers "are as strong as they were before" Reagan's threat and that the strike is still 81 percent effective. Legal Actions

U.S. District Court Judge Oren Lewis Alexandria ordered the first striking air controller to jail yesterday, sentencing Steven L. Wallaert, president of the PATCO local in Newport News and Norfolk, to 60 days for contempt of court. A federal judge in Kansas City, Kan., jailed four other union officials.

Meanwhile, court-ordered fines are rolling up against the union at the rate of millions of dollars a day. A New York judge fined PATCO $100,000 an hour, and a Washington judge has assessed progressive fines that will reach $5 million by the end of the week. The union has $3.5 million in a strike fund.

Federal prosecutors had obtained back-to-work injunctions in 57 cities, and judges has issued 39 criminal complaints and 20 civil contempt citations against union leaders and striking controllers. Air Traffic

The Federal Aviation Administration said up to 72 percent of regularly scheduled flights were taking to the air yesterday, with average delays ranging from 17 to 23 minutes, up to a maximum of 90 minutes, but the FAA was still limiting takeoffs from the nation's 23 laregest airports. Airlines reported that slightly more seats were occupied, but many would-be passengers were still avoiding air terminals because of delays.

Transportation Secretary Drew Lewis said the air traffic control system could run "relatively well" for a year or two, but added that there would be some public inconvenience. "This is no cakewalk," he said.

Airlines said the airlines was costing them ten of millions of dollars a day. The Contract

The government has vowed not to negotiate with PATCO while the controllers are on strike. When talks broke off early Monday morning, the two sides were more than $600 million apart, with the government offering a 36-month, $105 million package, and the union demanding a far more expensive contract that would have included a 32-hour workweek and a more generous retirement plan.

Secretary Lewis said the administration's emphasis now is not on renewal of contract negotiations but on "how we rebuild the system."