Reports from some of the nation's largest firms yesterday indicate profits during 1978 continued to climb in such diverse industries as steel, publishing and brokerages.

United States Steel Corp. reported 1978 income of $242 million ($2.58 a share), up from the top domestic steel producer's 1977 earnings of $137.9 million ($1.66).

Fourth quarter earnings soared to $94.6 million ($1.11) compared with $9 million (11 cents) in the fourth quarter of 1977.

Sales of $11 billion were recorded in 1978, compared with $9.6 billion in sales the previous year. Sales for the final quarter were $3 billion compared with $2.4 billion.

Shipments for 1978 amounted to 20.8 million tons, up 1.1 million tons from 1977, reflecting a greaterdamand for plates, sheet and strip, structural and tubular steel, the firm said.

The steelmaker declared a dividend of 40 cents per share on common stock, payable March 10.

Merrill Lynch & Co., parent of the world's largest securities broker, reported a 62.4 percent increase in profits for 1978, but said the pace of earnings gains eased in the final quarter of the year as stock trading volume slowed.

Merrill Lynch, owner of Merrill Lynch, Pierce, Fenner & Smith Inc., said fourth-quarter earnings were 15.1 percent ahead of those of a year earlier and totaled $9.1 million (26 cents a share). Revenues were $405.6 million.

Fourth-quarter earnings in 1977 came to $7.9 million (22 cents) on revenues of $304.5 million, Merrill Lynch said.

For 1978, Merrill Lynch earned $71.3 million ( $2) on revenues of $1.53 billion. Earnings in 1977 were $43.9 million ($1.25) and revenues were $1.12 billion.

The Merrill Lynch earnings report "was a little better than I was expecting," said analyst John B. Walthausen of the Value Line Investment Survey, an advisory service. Walthausen earlier this month had forecast Merrill Lynch's 1978 earnings would total $69 million, or $1.90 a share.

In a prepared statement, Merrill Lynch Chairman Donald T. Reagan and President Roger E. Birk said the firmhs fourth-quarter gains "were achieved in the face of slowed stock market volume... and sharp declines in the equity and fixed-income markets.

"Nonetheless, our commission revenues rose 43.3 percent in the fourth quarter from the 1977 levels," they said. They also reported gains from commodity and options trading, mutual fund operations and from investment banking.

Two companies being wooed in takeover bids, McGraw-Hill, the publishing giant, and Bulova Watch Co., reported improved earnings yesterday.

McGraw-Hill earned 77 cents a share in the fourth quarter, up from 64 cents a year ago, as sales rose to $219.43 million from $189.87 million.

For the year, McGraw-Hill earned $63.66 million ($2.57 a share) on sales of $761.2 million, compared with $51.39 million ($2.08) in 1977 on revenues of $659.02 million.

American Express Co. is seeking to buy McGraw-Hill for $40 a share.

Chairman Harold McGraw said he expects 1979 to be another excellent year for the company.

Bulova, which is being wooed by Loew's Corp., earned $3.51 million (94 cents a share) in the December quarter in contrast with a loss of $1.3 million a year earlier.

For the first nine months of its fiscal year, Bulova earned $8.28 million ($2.20) in contrast with a loss of $2.53 million a year earlier. Sales rose to $171.46 million from $154.43 million.

However, chief executive Sol E. Flick said Bulova might show a loss of about $3 million for the whole year because the final quarter is always a poor one for the watch company, and it has substantial fixed charges to meet during the fourth quarter.

Food Fair Inc., the supermarket chain that closed 123 stores last week, reported a loss from continuing operations of $4.35 million for the four weeks ended Dec. 16 on sales of $156.72 million.

Food Fair has been operating under Chapter XI of the federal bankruptcy laws since Oct. 2. It closed 89 stores in the New York metropolitan area in December, and the firm announced last week it would close 123 stores in Pennsylvania, Florida and New Jersey, idling 5,500 workers.

For the four-week period losses from the 89 stores in the New York metropolitan area closed before Dec. 16 were $4.03 million. For the 11 weeks after the company filed bankruptcy, until Dec. 16, total losses were $29 million; $11.89 million of the loss was from the stores closed before then.

The company has not reported on its operations for the last half of December or January, therefore the impact on earnings or losses of the closing of the 123 stores last week has not been disclosed.