It's "Nutcracker" time again. This Old World story has become an integral part of American Christmas and often serves as the childhood introduction to the theater. 1984 marks the 30th year of its establishment as a Christmas tradition with the production choreographed by George Balanchine for the New York City Ballet.

The Washington Ballet declared this Christmas season officially open last night with the first of this year's "Nutcrackers" at Lisner Auditorium. And certainly this ballet is an appropriate symbol for this season of magical expectation. In the Washington Ballet production this promise is fulfilled in snowy scenes of a Christmas party held at a gingerbread Christmas house, by a growing Christmas tree and a nutcracker come to life, and not least by a superb rendering of the Tchaikovsky score under the direction of Thomas Ludwig.

Things got off to a rather bumpy start with a ragged and seemingly under-rehearsed Act I. The battle between the Nutcracker and the mice was particularly muddled as was the second scene in the Snow Forest. Certainly this "Nutcracker" has come close on the heels of the company's Latin American tour. Some of the problems also seemed the result of a lack of stage experience and opening-night jitters by the large cast of Washington Ballet School children. No doubt these rough edges will be smoothed out over the run as members of the cast settle into their roles.

Indeed, by Act II last night things seemed better already. There were several outstanding performances in the Kingdom of the Sweets. Lael Evans' and William Batcheler's Coffee had a mysterious languor and exoticism. Evans showed a beautiful fluidity in motion and a grand elegance in repose. Robert Wallace invested his Mirliton with an outstanding ballon and a truly wonderful finesse in his epaulement and stretched line. Not the least of his virtues was a sensitive musical phrasing.

Lynn Cote as the Sugar Plum Fairy suggested the exquisite delicacy of a porcelain figurine, though her technical strength was also clear in her flashing fouettes. John Goding's Cavalier displayed a solid technique and attentive partnering and was much improved over last season.

Through its "Save the Nutcracker" campaign, the company has undertaken a gradual refurbishment of the costumes. Designed by Carl Michel, whose costumes for the Dance Theatre of Harlem's Creole "Giselle" have been winning him acclaim, the new costumes are being added over several seasons. The costumes unveiled this year for the little boys and several of the ladies in the Act I party and the tutus for the Snow Queen and the Sugar Plum Fairy were designed to blend in unobtrusively with the costumes that remain from previous years. Michel will also design new sets to be unveiled in 1985.

The "Nutcracker" will run through Dec. 29.