One of Public Broadcasting's most innovative and enterprising series is back on the air for its third season. Enterprise (PBS, Thursdays, beginning Jan. 19, 8:30-9 p.m., check local listings), with ye olde TV news commentator Eric Sevareid still placing his introductory stamp of approval on the project, premieres with a slightly shallow but still fascinating portrait of cable TV's most controversial entrepreneur, Ted Turner.
''Ted Turner and the News War'' focuses on this controversial executive's recent competitive victory over Satellite News Channel. The program is documented with visits to both Mr. Turner's Cable News Network and the SNC. The chief executives of both organizations speak their minds openly, often to the detriment of the other.
What is missing, however, is just a bit more background on Ted Turner, a quixotic personality who is alternately called ''the mouth of the South'' and ''the Henry Ford of cable TV.'' We see the mouth side of the man, but it would have been enlightening for ''Enterprise'' to show viewers a bit more of the Henry Ford side, too.
Future segments of ''Enterprise'' will investigate the crematorium business, the invasion of Japan by Kentucky Fried Chicken, the $120 million Westin Hotel in Boston. Wherever the American entrepreneurial system is working . . . or not working . . . ''Enterprise'' seems to be there, enterprisingly observing, recording, interpreting.