FROM its start four seasons ago, Inside Story on the Public Broadcasting Service has been the only regularly scheduled review of the media on television. Aside from a few journalism magazines, there is very little public self-criticism or self-examination in the news profession.
Probably the most chastening event in recent years for members of the news media was the American public's reaction to the news blackout imposed by the Reagan administration on the early days of the Grenada invasion: Surveys showed the public approved. Those surveys pointed up the fact that there seems to be a growing mistrust among Americans of the news media.
Since the recent demise of the National News Council, the role of ''Inside Story'' has taken on new importance. The council functioned as a kind of semiofficial watchdog.
Former Mississippi publisher and State Department spokesman Hodding Carter has been the anchor of the General Electric-funded ''Inside Story'' since its inception. Although there has been some criticism that the series has been uneven - often superficial and only occasionally hard-hitting - the fact is that ''Inside Story'' has been performing a major public service. It has helped keep alive the public's awareness that the news media - newspapers, TV, and magazines -are subject to error, misjudgment, and excess. And it has pointed up a need for external watchdogs to make certain that arrogance, ideology, and the profit motive are not allowed to distort the news.
One two-part program - concerning the difficulties correspondents face in getting news out of the USSR - has won this year's Overseas Press Club Edward R. Murrow Award (in the interest of journalistic fairness, I must now reveal that I served on the jury which chose that winner). In addition, there have been fine shows this year concerning Jacobo Timerman's return to Argentina and on the question of a reporter's obligation to interfere to prevent personal tragedy.
But there was also a rather laudatory program about TV anchors prominently featuring ABC newsman Peter Jennings. And now it has been called to the public's attention that, in addition to his commitment to ''Inside Story,'' Mr. Carter is under contract to ABC. He functions occasionally as a correspondent on ''This Week With David Brinkley'' and recently served as a temporary substitute for Ted Koppel on ''Nightline.'' Mr. Carter also writes a column for the Wall Street Journal.
Mr. Carter claims that his various, seemingly conflicting obligations do not affect his news judgment in any way. Nevertheless, there certainly is an appearance of possible conflict of interest. Even such a fleeting perception by the public - or Mr. Carter's colleagues - could do great harm to the credibility of ''Inside Story.''
Mr. Carter has indicated that he plans to cut back on his appearances on ''Inside Story'' and allow other anchors to alternate. But that does not seem to me to be an acceptable solution. To be effective, ''Inside Story'' must be perceived as cleaner than the proverbial hound's tooth.
Since Hodding Carter does not appear to be in financial need (having benefited from the sale of his newspaper), and since he has already proved his ability as a print and electronic newsman, it would seem that the greatest service he could now perform in his chosen profession would be to devote all his time and effort to ''Inside Story.''
In my opinion that would mean abrogating his contract with ABC and the Wall Street Journal. I am fairly certain that both organizations would be willing to release him for the greater good of the profession.
Such action would clear Hodding Carter of even the slightest suspicion of conflict of interest. It would leave him free to work full time at improving ''Inside Story'' and make certain that the show is universally perceived as the impartial media watchdog which many observers feel is needed. Otherwise, the series is bound to deteriorate into an ''Entertainment Tonight'' about the media.
If Carter cannot bring himself to divest himself of other journalistic obligations while he serves as a kind of electronic ombudsman, it is perhaps time for him to resign completely from ''Inside Story'' and allow somebody else with impeccable, nonconflicting credentials to proceed with the job he so admirably started. 'The Press Baron Who Would Be King'
Like almost everybody else in journalism, Hodding Carter wants to know the validity of Rupert Murdoch's seeming philosophy that ''all that matters is selling papers.'' In The Press Baron Who Would Be King (''Inside Story,'' Friday , April 27, and May 4, 9-9:30 p.m., check local listings for premieres and repeats) Carter traces Murdoch's career over three decades on three continents.
No rags-to-riches story, it is more like a riches-to-more-riches story: Murdoch is the scion of a wealthy Australian family. He inherited a small newspaper at 22 and now owns 80 publications throughout the world, including The Times (London), the News of the World, and the Sun in England; the Australian in Australia; and the New York Post, the Boston Herald, the Star, the Chicago Sun-Times, the Village Voice, and New York Magazine in the United States.
Although Murdoch refused to be interviewed for ''Inside Story,'' producer Margaret Jay (the ex-wife of England's ambassador ot the US) has found excellent film footage of Murdoch in which he claims that he does not interfere with his editors - unless their papers are losing circulation. ''A successful editor has total freedom,'' he says.
Only the first half-hour of the two-part, one-hour show was available at press time, but in it Carter managed to find many newspapermen who accuse Murdoch of gross bias. Harold Evans, who resigned from The Times, speaks out from Duke University, where he is now teaching journalism ethics. ''Murdoch has contempt for the public,'' he says, and ''he accuses establishment newspapers of being elitist because they're interested in truth, accuracy, and they have high-minded ideals, as he calls it.''
In the second segment, Mayor Edward Koch of New York endorses Murdoch as a ''first-rate, dedicated New Yorker.'' Murdoch's New York Post, Carter points out , endorsed Mayor Koch for mayor.
Carter also notes that the New York Post has lost millions of dollars - in part because department stores are reluctant to advertise in it - despite the fact that Murdoch's sensationalism has raised its circulation.
In Chicago, where 68 journalists quit when Murdoch took over, columnist Mike Royko, who also resigned, describe's Murdoch's papers as ''trash.'' Ralph Otwell , who resigned as editor, claims Murdoch's journalism ''goes counter to everything that journalism has been in this country. It refuses . . . to recognize that with the First Amendment there's an obligation to elevate standards and tastes instead of pandering always to the lowest common denominator.''
In summation, Hodding Carter predicts that ''Murdoch will probably pursue his own political line through his newspapers but his slogan that 'all news is entertainment' may have to be modified to make money in some US markets. What seems certain is that the empire will go on expanding.''
''Inside Story'' is a bit late with the Murdoch story - it could have been done at least six months ago. There's very little that's new in the show - most of what is said has already been said elsewhere. And most of the hard hitting is left to the interviewees. But Carter pulls it all together in a lively way that may cause a few million previously ''uninvolved'' people to sit up and take notice of what is happening to their own media.
And that's why it is vitally important that Hodding Carter clearly establishes the purity of the ethics of ''Inside Story.''