Prince Charles and Princess Diana were greeted by a giant Canada goose and beaver when they opened Expo '86 in Vancouver, British Columbia, yesterday. The prince, who was a navy pilot, was reportedly disappointed that he had to cancel his scheduled piloting of a remote-controlled flying saucer at the ceremony. Said Dale Kramer, who designed the craft, "We had expected the prince to pilot the vehicle from the ground and, as a pilot, he could have learned to do it in 30 seconds.

"At the last minute we were told by fair authorities there was no time. I think Prince Charles was disappointed, and I certainly was." The rain dampened things a bit too, but Expo President Jimmy Pattison said, "Well, if you don't get rain, it wouldn't be Vancouver."

The festival, which is the biggest in North America since Montreal's Expo '67, presents exhibits, food, dance and music from 47 countries. More than 150,000 people attended opening day, and city officials expect the bustle to continue throughout the summer. Playboy to Close Clubs

It appears to be the end of an American institution. Playboy Enterprises Inc. announced that it is closing its last three clubs -- in New York, Chicago and Los Angeles -- effective June 30, due to a decline in business. Playboy decided to close the clubs after its Empire Club in New York failed to attract new key-holders, despite millions of dollars spent on new marketing techniques.

"In light of its results and our assessment of its business potential, prudent business practice dictates the closing of the clubs in these three cities," said Christie Hefner, president and chief executive officer of Playboy.

The closings will not affect three franchised clubs in Lansing, Mich., Omaha and Des Moines, or the five franchised clubs outside the United States. Playboy is exploring expansion possibilities for in-hotel franchise clubs in the United States and overseas. The company has been operating clubs for 26 years, and a spokesman said that "hundreds of thousands" of key-holders will be affected by the closings. Picasso in Pieces

David Robertson and Stefan Panylyk, owners of a mail order company in Sydney, Australia, said they plan to cut a signed print by Pablo Picasso into 500 one-inch squares and sell them for $135 apiece. "The idea is to give ordinary people a chance to own a piece of work by the century's greatest artist," said Robertson.

The two men bought a signed 1959 linocut print titled "Trois Femmes," valued (in its original state) at $10,000. Art dealer David Cook, who sold them the print, said he was appalled when he heard of the plan. "The guy walked in, said he wanted to buy a Picasso," Cook said. "Had I known what he was going to do, I never would have sold it."

Panylyk said they announced the sale in newspapers yesterday. He said each piece would be framed and would include a certificate of authenticity and a 30-day money-back guarantee. "We've already got 20 firm orders from calls this Friday morning. At this rate, we'll be chopping the print this afternoon."

Said Robertson, "If this thing takes off, we may buy other masters as well and give them the chop." End Notes

Society photographer Patrick Lichfield, first cousin to Queen Elizabeth, and his estranged wife Leonora confirmed yesterday that they were seeking a divorce. Commenting on a report that the divorce would be "totally without acrimony," Lady Lichfield said, "That is perfectly true, but it is very distressing. I do not want to say any more about it." She and her husband were married in 1975 and have three children . . .

A Rome court yesterday sentenced Italian film director Franco Zeffirelli to one year's imprisonment and fined him $566,000 on charges of breaking foreign exchange regulations. Prosecution lawyers argued that Zeffirelli, who officially became a resident of Tunisia in the late 1970s, had continued to work and live primarily in Italy and thus was subject to Italian exchange regulations. The director's attorney said he would appeal the verdict . . .

He may not be on the official payroll, but former president Richard Nixon is a frequent adviser to President Reagan, according to Fred Barnes, a senior editor for The New Republic. In the May 19 issue, Barnes writes, "Since the weeks before last November's summit in Geneva he's Nixon become a regular adviser of President Reagan, by telephone, on Soviet-American affairs." -- Lisa Serene Gelb