Profits increased slightly for the Washington Post Co. in the fourth quarter last year compared with 1979 levels, the communications firm reported yesterday.

Not counting a one-time accounting change that reduced final net income in 1979, however, the Post Co.'s profits from its diverse business operations for the full year were off 20 percent.

In another corporate report yesterday, UNC Resources of Falls Church listed a loss of $1.9 million in its third fiscal quarter ended Dec. 31 but predicted that the fourth quarter would be profitable.

The Post Co. attributed reduced earnings from operations to "substantial first-year losses" of the new Inside Sports monthly magazine and to expenses of The Washington Post's new satellite printing plant in Fairfax County.

In the recent quarter, Post Co. earnings rose to $15.4 million from $14.7 million a year earlier as revenues rose 7 percent to $185 million. Per-share earnings rose more sharply in the quarter, to $1.10 from 98 cents, because there were about 1 million fewer shares outstanding at the end of 1980. b

Profits earned from operations and investments in the year, not counting the special charge in 1979, declined to $34.3 million ($2.44 a share) from $43 million ($2.75) the previous year, while revenues increased 11 percent to $659.5 million.

In 1979, a one-time charge of $13.5 million (86 cents) reduced final net income to $29.5 million ($1.89). This special charge reflected the cumulative impact on prior years of a change in the firm's accounting for magazine subscription procurement costs.

Martin Cohen, vice president and treasurer of the company, said losses of the sports magazine were about $12 million for the year -- in line with recent estimates but higher than an $8 million start-up loss forecast originally. The magazine was started in March, and advertising business for most magazines has been soft because of national economic weakness.

Post Co. Chairman Katharine Graham said in December that the firm expects losses in 1981 to be "substantially less" for Inside Sports, which had an average circulation in the last six months of 1980 of 500,000.

At The Post newspaper, depreciation and other operating expenses associated with a new printing plant in Springfield reduced profits by about $5 million.

Overall, pretax profits fell in all three of the firm's major divisions -- broadcasting, newspapers and magazines. Revenues from newspapers in Washington; Trenton, N.J.; and Everett, Wash., rose 14 percent to $311 million, but pretax profits declined to $32 million from $35.4 million. Television station revenues were up 11 percent to $80.5 million as pretax earnings dipped to $22.1 million from $22.4 million.

The magazine division, which publishes Newsweek, reported an 8 percent increase in revenues to $268 million and a decline in decline in pretax profits to $11.5 million from $22.6 million. Post Co. equity in earnings of affiliates fell from $3 million in 1979 to $700,000 last year, reflecting a $2.5 million increase in the company's share of losses at a new Virginia newprint factory that opened late in 1979.

UNC Resource's third-quarter loss of $1.9 million contrasts with profits from continuing operations in the previous year of $2.8 million (26 cents a share). In the 1979 quarter, UNC took a one-time charge of $2.65 million against earnings because of discontinued business operations. That reduced net income to $122,000 (1 cent). Revenues declined to $49.1 million from $71.8 million, reflecting a sharp drop in uranium deliveries by the Falls Church firm.

In the nine months ended Dec. 31, UNC reported profits of $9.2 million (86 cents) compared with $12.9 million ($1.20) before the loss from discontinued operations in the 1979 period. Final net income for the prior year's comparable nine-month period was $7 million (65 cents).Revenues rose to $206 million from $205 million, with $29 million of 1980 revenues added from the sale of coal mining operations.

President Keith Cunningham said yesterday that further improvement is needed in reducing uranium production costs.