Five months after its long-awaited and much ballyhooed opening, the National Aquarium in Baltimore has received more than 713,000 visitors through its turnstiles by the city's glistening Inner Harbor, far exceeding early expectations and stretching the facility's resources right up to and beyond its limits.

Patrons have grumbled over two hour waits outside on peak days and complained about too many people inside to enjoy the exhibits. Security needs have increased, corridor carpets have worn down and along with an overworked staff there is the problem of fatigued fish.

Almost every night since the middle of September, after the daytime crowds have gone home along with most employes, the fish have been forced into overtime. The aquarium, it turns out, has become a chic setting for charity events, corporate feasts and political fund-raisers. People gather in the Harbor View Room, in the lobby and by such exhibits as "Surviving Through Adaptation" to eat buffet dinners, sip wine and gaze at the 4,000 fish.

Black & Decker, McCormick Spice, Bethlehem Steel, local banks and investment houses, Hadassah and the Enoch Pratt Library have been among the sponsors of the functions, some of which have spilled over from the nearby convention center with as many as 1,800 at once jamming the aquarium. Maryland Attorney General Stephen Sachs and House Speaker Benjamin L. Cardin held fund-raisers by the fish, and former governor Marvin Mandel attended a function there sponsored by a corporation shortly after his release from federal prison.

"We're the newest place in town to give an impressive party," said Shirley Polikoff, an aquarium volunteer who works on party arrangements. "We try to tell people this is not their right place, that this is not a ballroom or a country club, but they insist. I guess we are the sexiest place in town."

The fish, however, were not adapting well to the constant glare of lights that lasted well past midnight as the mopping up crews came in to clean up the evening's debris, according to officials. The "critters," as they are known here, weren't getting enough sleep. In 1982, it has now been decreed, nighttime festivities will be restricted to two or three evenings a week so the fish can rest.

"Our success has been a bit overwhelming," said William S. Flynn, the acting director, who can hardly wait for a permanent director to be hired so he can return to his primary job of worrying about fish instead of finances and personnel and carping critics. "A $25 million project opened in a crash situation. We're damn proud of what we did."

Still, there have been problems, especially with personnel. Several high-level employes, including the director, have left for a variety of reasons. Aquarium officials have had to triple the security force to 18 full-time employes, increase the number of janitors, and assign as many as eight secretaries full time to handle a flood of applications for annual memberships that now number some 23,000.

Aquarium officials say they are committed to operating the facility without subsidies from city taxpayers, who are paying for construction of the modernistic building through repayment of revenue bonds. So far, the officials say, revenues are running high enough to turn a profit beyond first year expenses of about $4.4 million.

To assure the aquarium's financial success, officials have solicited corporate sponsorships of special tanks and "Aquadoptions" of specific fish and birds in the aquarium's tropical rain forest by individuals, groups or businesses. Among the "Gold" contributors, donating at least $5,000 each, are the Maryland National Bank, sponsor of the Seal Pool; the Marriott Corp., which is sponsoring the Dolphin Tray; and two utilities, Baltimore Gas & Electric and C&P Telephone Co., sharing the $25,000 sponsorship of the Coral Reef Tank.

Every tank has a sponsor except the sharks'.

"We even went to a few lending institutions, in the spirit of humor," said Cathy Cloyd, the aquarium's marketing director. "They didn't see the humor in it." Trying another tack, officials changed the name of the shark tank to the Open Ocean Tank, without results.

The "Aquadoptions" attracted 4,000 "parents" last year, each of whom received a fancy certificate and "Fin-Pal" letter, in return for contributions ranging from $15 for a spider crab or menhaden to $3,000 for a blue and gold macaw or pavonine quetzal. "There are plenty left, especially in the shark categories," said Kathy Marinari, who keeps tracks of such things.

The "Aquadoptions" have, like the Harbor View Room, caught on. The board of directors of the Baltimore City Fair gave Mayor William Donald Schaefer a "seal of approval." Radio Station "98 Rock" adopted a rockfish. For $2,500, Black & Decker, the hand-tool manufacturer, adopted a sawfish.

The program, which has raised $120,000 so far, is being reassessed. According to Marinari, the costs of mailing and printing are enormous, although "it's hard to measure the PR value, which is good."

Promotions aside, officials have been hard-pressed to handle the large crowds that began forming as soon as word spread of what Time magazine called the "aquarium's orchestrated splendors." Mimes and clowns helped a little, but most of those waiting in line for admission--60 percent from outside the Baltimore area--said not much, according to staff surveys.

To speed up the line, more people were admitted sooner. Consultants claimed the building could comfortably handle up to 1,200 an hour, but the more the merrier was not the case. Now, a traffic pattern of 750 to 800 an hour is the rule, with resulting long lines again on peak days. "Last week was chaos," sighed Frank A. Gunther Jr., the harried chairman of the board who wears a whale tie and dolphin tie clip.

Can it last forever, this seemingly endless line of fish fans? Baltimore promoters expect the number of tour buses coming to town this summer to double, and the aquarium plans to expand by 200 its current volunteer force of 350. Flynn, with 26 years "in the business," predicted, "There'll be lean years, like any other industry. We don't know what's down the line. But while it's fat city, we hope to take advantage of it."