There's a group of movie critics that the public knows little about, yet it has a sometimes important influence on movies the public sees: the anonymous military officers in the Pentagon who decide whether a movie maker will get official cooperation that could save millions in production costs.

From our examination of a series of documents that detail the confidential negotiations between Hollywood and the Pentagon, we have come to the following conclusions:

The Pentagon gives its wholehearted cooperation only to those producers who agree to turn out the equivalent of a recruiting poster.

If a producer acts like a doormat to get the military reviewers' approval and cooperation, the Pentagon will walk all over him and demand changes that could significantly affect the artistic integrity of the movie.

There's an inverse principle of military movie making: the less support (and interference) a producer gets from the Pentagon, the more likely it is that the movie will be a critical and/or commercial success.

In short, this unholy, unhealthy alliance between Hollywood and the Pentagon -- so often eagerly sought after by each side -- is usually to the advantage of neither, and is certainly not useful for the American public, which pays for the movie in both subsidies and at the box office.

Perhaps the best confirmation of these conclusions is that the total level of Pentagon support for the Vietnam War movie ''Platoon'' was exactly zero. Yet it was both a critical and a commercial success of prodigious proportions.

The low-budget ($6 million) film was a blockbuster at the box office and won four Oscars, including ''Best Picture'' and ''Best Director.'' Its success was a tribute to Oliver Stone's dogged loyalty to a script he wrote in 1975, based on his own combat experience in Vietnam -- a script that was rejected by all the major studios.

The ''Platoon'' script was also rejected by the Pentagon. In a confidential memo dated June 28, 1984, Col. John E. Taylor of the Army's public affairs staff wrote:

''We have reviewed the script, 'The Platoon,' and have found the Army cannot support it as written. In its present form, the script presents an unfair and inaccurate view of the Army.

''There are numerous problem areas in the script. They include: the murder and rape of innocent Vietnamese villagers by U.S. soldiers, the coldblooded murder of one U.S. soldier by another, rampant drug abuse, the stereotyping of black soldiers and the portrayal of the majority of soldiers as illiterate delinquents. The entire script is rife with unrealistic and highly unfavorable depictions of the American soldier.''

Donald E. Baruch, a top Pentagon public affairs official, concurred in a July 5, 1984, letter. ''In our opinion,'' he wrote, ''the script basically creates an unbalanced portrayal by stereotyping black soldiers, showing rampant drug abuse, illiteracy and concentrating action on brutality.''

Baruch left the door open for compromise: ''Of course, we would be delighted if your company would consider screenplay revisions. A meeting can be arranged to go over the script, if someone wishes to come to Washington.''

As it happens, all objections raised by the Army censors were aimed at the very features of the movie that eventually drew critical acclaim, led to its commercial success and brought widespread testimony from Vietnam veterans that the story of their war had finally been told as it was.

Admittedly a movie doesn't have to be a critical smash to get the thumbs down from the Pentagon. It refused to cooperate with Sylvester Stallone's ''First Blood,'' a gory action adventure that was a smash with the public and a bust with the critics.

The Pentagon also refused to cooperate with the makers of another Vietnam film, ''The Deerhunter.'' Other Pentagon rejects included Arnold Schwarzenegger's ''Commando'' (for ''implying that the U.S. Army has or had a special unit trained solely for the purpose of committing murder and pillage''); ''War Games'' (because no computer hacker could break into the military's strategic defense system); ''An Officer and a Gentleman'' (because the Lou Gossett character and the portrayal of boot camp were offensive) and ''Heartbreak Ridge'' (because the profanity and other attributes of the Clint Eastwood character were offensive).

The one notable exception that proves the rule was ''Top Gun,'' which succeeded even with the Pentagon's enthusiastic cooperation.