"Inside Story," a new public TV series about the press, seems a model of instant expendability. The program begins its run tonight at 8 on Channel 26 with Hodding Carter rattling on about what journalists should and should not do. One thing they probably should not do is sit in front of a mirror making faces at themselves on shows like this.

The project never sounded very promising, and as executed the program has the flat, stale pallor one associates with television by committee, public television especially (no fewer than 10 underwriters are listed as having scrounged up the production costs). It lacks punch and immediacy, and Carter, a journalist -- apparently still hot for the limelight after his turn as a State Department spokesman during the last administration -- has a video presence both lulling and pretentious.

Three minutes out of the first half hour are worth saving. Bob Elliott and Ray Goulding, the priceless and incomparable perfectors of no-fault comedy, offer a brief sketch in which a fired-up investigative TV reporter learns to his chagrin that the killer ice cube trays he's looking into went out of production years ago. Unfortunately, even Bob and Ray get gimmicked up, perhaps by executive producer Ned Schnurman. Bob and Ray work best simply sitting and talking together; in an effort to add extraneous movement, they're required to amble about a set and adapt to various camera angles. Ray looks overly dependent on cue cards.

The major piece on the program explores the media circus that has attended, if not engulfed, the tragic situation in Atlanta, where the slaying of 26 black youths since mid-1979 has become a continuing national story. "The growing press attention to these deaths has focused more on the spectacle and the sideshows than on the deaths themselves," Carter says.

"Inside Story" was upstaged on this aspect of the story, however, by "The CBS Evening News with Dan Rather," which aired Bruce Morton's excellent, powerful and succinct report last Friday. A clip from the March 26 Rather News, in which CBS had to admit that a lead on the killer proved fruitless, is included in the "Inside Story" segment.

Such examples are helpfully illustrative, but the program keeps lapsing back into Hodding pudding -- soporific ruminations by Carter, the all-seeing eye. "What finally can be said about the sorrow and the spectacle in Atlanta?" he asks ominously. Ugh.

A segment called "Hits and Misses" (The New York Times refused permission to use the in-house term "Winners and Sinners") also proves a fizzle, although Elizabeth Coleman, a producer and reporter, has a TV speaking style that is pretty funny. Her head bobs from side to side as if she were the hostess on "Romper Room" inviting one and all to man the jolly jump ropes.

Among the "Hits" cited in this segment is the investigative work done by a Minneapolis station that shadowed a housing inspector one day and found he didn't do any work. The man, it is cheerfully reported, was subsequently fired. Score one big victory for the sanctimonious Fourth Estate.

The final segment is called "Viewpoint," with Carter holding forth still further on media matters of lofty import. A dramatic clip is shown of ABC's Frank Reynolds on the day of the Reagan shooting, after it was learned that broadcast reports of White House press secretary James Brady's death were erroneous. "Let's get it nailed down, somebody; let's find out!" Reynolds barked.

Some said at the time it was a mistake for Reynolds to lose his composure. It turns out that it enhanced his personal popularity more than ever.

"Inside Story" doesn't get into such vulgar matters as popularity of newscasters, though, preferring to play address-the-issues in about as pompous a way as is imaginable. Although frequently keeping an eye on TV attention spans, it never gets as far below the surface of anything as would obviously be advisable. The show might be better off staged as the kind of shirt-sleeve donnybrook thrown each Thursday night locally on WDVM-TV's entertaining bloodbath "After Hours," with Patrick Buchanan and Tom Braden.

"Watching the Watchdog," recently produced and aired by CBS-owned WBBM-TV in Chicago, was a more sophisticated and valuable fit of journalistic soul-searching. But it's worth wondering if the public has much interest, or ought to have much interest, in a project as implictly narcissistic as "Inside Story" in the first place. Most good journalists are rigorously self-critical, even self-loathing in some extreme cases, and it doesn't take a crisis to get the housekeeping mechanisms of journalism rolling.

In other words, even if it were splendidly done, "Inside Story" would be of dubious use. As it has been done -- pedantically and without a convincing sense of purpose -- it is of no apparent value.