Striking an upbeat note on its last day in office, the Carter administration yesterday announced that the summer beaches can open on Lake Erie where once the algae bloomed; that salmon may be caught for the first time in 100 years on the Connecticut River; and that lead poisoning is no longer a danger from Boston city water.

The Environmental Protection Agency, in a thick, glossy, lushly illustrated report, allowed itself to brag a bit about the accomplishments of the past 10 years, a period many call the decade of the Environment. In case studies from around the country in every field of conservation and cleanup work, EPA provided what Administrator Douglas Costle called "a glimpse . . . an effort to show that there is hope."

The progress reports are "emblematic of the national effort" in "the first generation of pollution problems," Costle said, and do not mean everything is now squeaky-clean.

"There are few unqualified successes," he wrote, "and even greater challenges lie ahead." Ultimately, he said, "we must look beyond pollution abatement to the more sophisticated arena of pollution prevention."

To pick the success stories, EPA used three criteria: firsthand evidence of progress, such as visibly cleaner air or quieter streets or clearer water; decrease in the measured concentrations; or decline in volume of pollutants. It found several hundered sites worth noting.

The Connecticut River: Although there were what one 1783 chronicler described as so many salmon in the river that "no finite being can number them," sewage, high dams and heated water from utilities and factories did them in. The last one was caught in 1874. But sewage treatment plants were built, along with fish ladders, and restocking began in 1968. No luck. The water was still too polluted.

After the 1972 Clean Water Act amendments, however, utilities put out cooler water and industrial effluent faded. An eight-pound salmon was caught in 1977, and more have come in every year since then.

The Cuyahoga River: Once so polluted from steel milling and chemical waste that it actually caught fire, the river's lower end had a bacterial count that equaled raw sewage. Now 17 sewage treatment plants have gone up, there is no more oil on the surface, and phosphorus levels have been halved. Although there is still a lot of floating junk and the sediment is still so contaminated that the lower end "will still have difficulty supporting anything but the most pollution-tolerant forms of aquatic life," EPA says Ohio's Cuyahoga is "significantly improved."

Lake erie: The sickest of the five ailing Great Lakes is showing "some signs of progress," although "most of the job still lies ahead." Blotched with green slime patches and virtually lifeless in 1970, the lake's border states and Canada cut their DDT use and (except for Ohio) banned use of highphosphate detergents. Some fish now live in the lake and Sterling State Beach Park has reopened for summer swimmers.

East Coast: Where 150 industries and 250 sewage treatment plants once dumped their sludge off the coast of New York and New Jersey, causing a 25-mile-square dead sea, only six factories and 20 sewage plants do so now, and all must stop by 1982.

Boston: A 1974 sampling found lead levels up to five times the permitted level in Cambridge, Mass., drinking water, with comparable levels in a third of area homes. Corroded plumbing was given a chemical bath that brought lead down below the federal standard.

Florida: The citrus industry used to dump its wastes in the nearest water, causing fish kills and odors. After World War II the peels and pulp were diverted to cattle feed, and now the industry is beginning to recycle its liquid waste, spraying some of it back on the groves and putting some in activated sludge to make fertilizer.

Gary, Ind.: The "red sky city" had 2 1/2 times the permitted air pollution level from its steel mills and "still has far to go," but compliance efforts have shrunk considerably the area that breathes Gary's fumes.

Arlington, Va.: The Pentagon's computer-matched car pooling system, set up in 1973, involes 18,000 employes and 5,000 cars and has kept 2,000 cars off the rush-hour roads.

Atkinson, Ill.: A town-owned hazardous-water landfill, set up at an abandoned strip mine, is not only beautifying the mine but has paid for itself, for schools, road repairs and other city services.

Allentown, Pa.: As part of EPA's Quiet Communities Program, citizens in 1977 did a noise assessment study, came up with a plan to reduce the racket, passed a noise control ordinance and are enforcing it. The reward: five decibels, the average level of noise reduction so far.