The stock market continued its broad slide yesterday in what analysts were calling the summer doldrums. Climbing interest rates continued to be paramount among investor concerns.

The Dow Jones average of 30 industrial stocks ended the day down 7.10 points at 805.79. This was the lowest close since April 16, when the market was just beginning its high-volume spring surge.

Declines outnumbered advances by more than 3 to 1 on the New York Stock Exchange.

The Dow had been off nearly 10 points, threatening to pierce the 800 barrier, but recovered a little towards the close. Volume on the Big Board was 23.7 million shares, up from Monday's molasses pace when only 11.6 million shares changed hands prior to the July 4th holiday.

With economic forecasts of a recession by early 1979 becoming more widespread, analysts said investors were biding their time while looking forward to what they hoped would be the onset of a mild recession that would allow interest rates to peak and take some pressure off inflation, while doing minimal damage to corporate profits.

"Let's get the recession started so we can get the bull market begun," commented Larry Wachtel, vice president with Bache Halsey Stuart Shields.

But James Balog, senior executive vice president at Drexel Burnham Lambert, said he was not so sure that a recession was in the offing.

"There continue to be some very strong elements in the economic picture," said Balog, citing continued high levels of consumer spending, growing capital investment and a lean inventory-to-sales ratio for business firms. "Maybe it all adds up to the fact that the economy will surprise us."

Meanwhile, he said, investors were seeking more information on the outlook and would continue to deploy their assets in short-term money market instruments until the likelihood and extent of a recession becomes clearer. That means "the market will go sideways until we resolve some of the uncertainties," he said.

Balog and other analysts put a bottom on the market's current slide at about 780 on the Dow.

Gambling-related issues continued to show pep yesterday, as Resorts International, which has opened the first and so far only casino in Atlantic City, N.J., reported that its gross revenues from the casino exceeded $16 million in June.

Allegheny Airlines, which is the only carrier certificated to serve Atlantic City, was the Big Board's most active issue, gaining 1/2 to 10 1/2 on a turnover of 314,000 shares.

Playboy Enterprises was the biggest percentage gainer on the NYSE, rising 3 5/8 to 25 1/2.

Resorts International class stock jumped 12 3/4 to 86 on the Amex on the news of its take. And Resorts B was up 12 to 90.

Memorex dropped 1 3/8 to 47 7/8 while IBM rose 3/4 to 257 1/2. A mistrial was declared in Memorex's 309 million lawsuit against IBM.

The broader NYSE index dropped 0.46 point to 53.00.

The American Stock Exchange index, meanwhile, was down 0.64 point to 144.90. Losers outnumbered gainers by 2 to 1.

And the NASDAQ composite index of over-the-counter stocks dropped 0.93 point to 119.22.