Dart Drug Corp.'s profits plunged 60 percent last year, and earnings of Giant Food Inc. were essentially flat, the two major Washington retailers reported yesterday, providing further evidence of how badly retail business was hurt by the downturn in the economy.

Dart's profits dropped from $3.56 million ($2.04 a share) to $1.38 million (83 cents), including the special write-offs for closing Dart's four stores in Richmond. Dart sales increased 12 percent to $259 million from $231 million for the year ended Jan. 31, while Giant's sales climbed 19 percent to $1.48 billion from $1.24 billion for the year ended Feb. 28.

Giant's net income increased to $18.3 million ($3.74 a share) from $17.86 million ($3.64). Giant officials pointed out that earnings got an unusual boost from the company's accounting method which every fifth year uses a 53-week fiscal period; 1980 was a 53-week year, and the extra week added an estimated 20 cents to 30 cents a share to profits.

Giant's 19 percent sales gain was well in excess of the increase in food prices last year, indicating the chain was able to improve its share of the Washington-Baltimore supermarket business by building new stores and launching an aggressive sales promotion plan.

For its fourth quarter, Giant earned $10.3 million ($2.10) on sales of $514.7 million, up from $6.47 million ($1.36) on sales of $418.4 million last year.

Dart's fourth quarter produced earning of $121,000 on sales of $74 million compared with profits of $1.26 million on sales of $66.9 million.

D.C. National Bank and Security National Bank, the seventh- and eighth-largest in Washington, reported sharply higher earnings for the first quarter.

D.C. National profits were up 63 percent to $592,000 ($2.82 a share) from $362,000 ($1.77) last year. Security National earnings jumped 29 percent to $626,000 ($1.57) from $486,000 ($1.21).

Bresler & Reiner Inc., a Washington real estate developer and builder, reported a 343 percent increase in profits for 1980 due to a $1 million profit on the sale of land and interest income on mortgages on properties sold the previous year.

Chairman Charles S. Bresler said the firm posted net income of $1.23 million ($1.11 a share) on revenues of $10.7 million compared with $357,000 (32 cents) the year before on revenues of $13.7 million.