The president and Mrs. Reagan began a marathon of ball-going last night with a visit to the American Legion's banquet in a capital celebrating both the inauguration and the hostages' freedom.

Something of a squabble developed between the political stars and the television stars at one of the inaugural balls last night, but Pat Boone kept right on singing and so nobody noticed. What happened was this:

Actress Carol Lawrence was supposed to sit in a prime box near the stage set up at the American History Museum, but that's where Jeb Bush, vice presidential son, thought he was supposed to sit. Well, one thing led to another, and pretty soon Carol Lawrence's people were firmly escorted to another area.

"Some guy told me he was going to knock me on my ---," said a ruffled member of the Inaugural Committee named Jack Caussin. He is also a retired Marine, and told people this. "But I'll still knock anybody on his --- that is going to knock me on mine," he added.

Soon enough, things became pleasant again. "This is a better box anyway," said Lee Mimms, Lawrence's manager, referring to their new habitat. "Television will get this box."

Everyone else, squashed right up against exhibits that said "Everything you always wanted to know about pendulums but were afraid to ask," seemed to be having a grand time. This was the ball for a lot of Midwestern states, although you could still find a few of the locals.

Like Caroline Wagner, a 25-year-old Department of Energy employe from Annandale who spent the day listening to hostage news on the radio and sewing her ball gown.

"My date came and I was still sewing the straps on," she said."I was going to put a bustle on the back, but I didn't get a chance to. Anyway, it's finished enough. I figure I just won't turn around."

Three hours later, ruffles and flourishes: The president!

He spoke of the hostages. "I am happy to say now," he said, "that they are only minutes away from landing in Wiesbaden, West Germany." The crowd cheered. Yelled. Even screamed a little.

Then Ronald Reagan turned to the first lady and said, "Do you mind if I have the last dance?"

Afterward, she kissed him.