DID THE wife of Chile's military dictator Augusto Pinochet slip into Detroit incognito to watch the Republicans nominate Ronald Reagan?

Lucia Pinochet was in Washington with an entourage for a few days earlier last week, staying at the Four Seasons hotel under heavy security, using an assumed name. Arrangements were made by the State Department and even most top hotel employees were unaware of her real identity until her party had checked out.

Members of the Chilean community in Washington got word that Mrs. Pinochet was en route to Detroit where her husband's regime has many friends.

But if she showed up in Detroit she kept a low profile. The State Department had a large contingent of ambassadors and other VIPs at the convention as pampered observers. But Mrs. Pinochet was not part of that official group which lunched with Mayor Coleman Young at his official residence and dined with Pepsico president Donald Kendall at the Renaissance Club before Thursday night's final session.

Sources at both the State department and the Chilean Embassy claim Mrs. Pinochet had gone straight back to Chile from Washington.

She likes to shop in Washington and reportedly comes at least once a year. She was last in the nation's capital in September 1979, staying at the Embassy Row hotel, only three blocks from the site where her husband's regime had blown up former Chilean ambassador Orlando Letelier in 1976.

Mrs. Pinochet, who wears modest cotton dresses when she works among the peasants in Chile, likes American designer clothes and "House and Garden" furnishings.

One of the stars of the Republican convention will be headed for New York in three weeks for a repeat performance among the Democrats.

Joyce Garrett, described by the Detroit press corps as "the long-time social companion" of Detroit Mayor Coleman Young, will be checking into the Essex House with him and others on his staff.

They got a good hotel because of his early support for President Carter's reelection. Young is also chairman of the Democratic Party Platform Committee.

Garrett, a 1953 Smith College graduate, who majored in government, is a controversial figure in Detroit, earning $40,000 a year as information director. Young had been planning to raise her salary to $48,000 but had to back down recently when his critics started sniping.

She was everywhere with him last week, greeting the press on his yacht in a flowing white lace caftan and welcoming Nancy Reagan and the diplomatic corp to a luncheon by the swimming pool at the "Manoogian mansion," the Mayor's official residence.

Both Garrett and the mayor are newly-slim, taking themselves off to "La Costa" in California, to lose weight before the two conventions.

Garrett recently redecorated Manoogian mansion, where a six foot oil portrait of her in flowing white chiffon hangs in the drawing room. But for some reason she and the mayor did not seem anxious to show off the house's new look.

The luncheon for diplomats was held entirely outdoors in a garden where horticulturally perfect perennial beds and terraces overlook the Detroit River. Guests were discouraged from going inside even to use the powder room or to call a cab.

Astonished diplomats found themselves directed by a large painted sign to a unisex toilet in a three car garage which was reached by climbing over cars, lawnmowers and garden tools. The facility had no lock on the door and it had obviously been installed decades ago for chauffeurs and gardeners and apparently had not been cleaned since.

One ambassador who declined to use the facility with a shudder, came out of the garage muttering, "Did someone say the Detroit millionaire who gave this mansion to the city made his money in plumbing?

Ronald Reagan is not his daughter Maureen's only candidate. She had been wearing a button quoting "Barnae for first dog." Barnae is the "Dach-a-poo" -- part dachshund and part poodle -- she picked up as a stray in Texas years ago and for whom she gives an annual birthday party.

Michael Reagan is wearing an Iranian hostage bracelet he says he got from "Faith Church" which he attends. It's really Faith and Evangelical Church but Reagan says he shortened the name because he has a hard time saying "evangelical." He told a reporter that "the only time I've ever pronounced it correctly was when I said it to you just now and it took me three times to get it right.

The eighteenth floor of the Ponchartrain Hotel is where the management put its VIP guests. If someone set off a fire alarm in the wee hours of the morning outside John Chancellor's suite hoping to get a look at him in his pajamas they were disappointed. When the persistently clanging alarm caused guests to finally pour out of their rooms and into the corridors, most were in their nightclothes, but a fully-dressed Chancellor stood calmly puffing on his pipe until security guards assured everyone that it was a false alarm.

As Maryland Sen. Charles Mathias came through a reception line here at the Renaissance Center, his host, Pepsico president Don Kendall, said, "Let me get you a diet Pepsi." Mathias, who has put on weight, sucked in his stomach, threw back his shoulders and tried unsuccessfully to button his jacket. Laughing, he conceded: "Well, I guess that IS what I need to start drinking."