The only regularly scheduled prime-time television study of the media needs more air time to present its studies. Inside Story (PBS, Friday, Feb. 10, 9-9:30 p.m., check local listings for premiere and repeats), with anchor man Hodding Carter in charge, takes an interesting, if slightly superficial, look at Chicago's black mayor, Harold Washington, and his relations with the media, especially with local CBS newsman Walter Jacobson. It's not a good relationship.
Mayor Washington insists that the press doesn't understand the black perspective and, in fact, states that he doesn't believe any white press will ever do so. At one point, Mr. Carter points out that many cities have ''ethnic'' mayors, some of whom do get along with the media and some of whom do not, depending mainly upon their own personalities and ability to cope.
''Black Pols/White Press'' barely scratches the surface of this story. What's missing is a solid interview with Mayor Washington, some information on media persons other than Jacobson, and some more in-depth analysis by Hodding Carter, a man with much stronger opinions than he seems to be willing to express on ''Inside Story.''
What would solve the problem, I suspect, is at least a half-hour more time for Carter to develop his studies and comment in greater depth. General Electric , which funds the half-hour show, should consider extending its grant so that an expanded ''Inside Story'' would be able to really sink its teeth into stories rather than merely nip at the heels.