Peter Breastrup's The Big Story: How the American Press and Television Reported and Interpreted the Crisis of Tet 1968 in Vietnam and Washington is the classic study on the reporting and its effect on policy. It is a very good book. There is a review of the book here.

Here are a few excerpts from the review:

The sheer volume of press and TV reports on Tet is intimidating, and, of course, almost every conceivable interpretation of events can be found in them. Nonetheless, Braestrup's analysis points to the emergence of several themes that came to dominate the coverage. The sober examination of these themes with hindsight reveals important misconceptions.

Misconception: There had been no warning of a coming offensive. Actually, the press ignored cautions expressed by General Earle Wheeler and General William C. Westmoreland in December and January.

Misconception: The offensive was a victory for Hanoi. The press corps, it is now clear, was stunned by the initial Tet attacks, many of which occurred in Saigon. When the allies met some initial reverses, the press reacted by emphasizing the enemy's successes. As the weeks wore on and military intelligence clearly indicated defeat for the insurgents, the press still interpreted the offensive as a "psychological victory" for the Vietcong/ North Vietnamese Army, who "held the initiative," "decide who lives and who dies... which planes land and which ones don't," who were unconcerned with losses, and could "take and hold any area they chose." There was little objective analysis of the many enemy failures or of the severe toll that allied counterblows exacted from the enemy.

Misconception: The North Vietnamese military initiative bared the unreliability and inefficiency of our own allies, the South Vietnamese. Government of Vietnam (GVN) troops were described as "lolling in the sun," failing to carry their load, and complacent. The press reported that the offensive shattered GVN control over the countryside and conclusively undermined the loyalty of the people.

A more truthful assessment: the GVN "muddled through" the crisis, Army of Republic of Vietnam (ARVN) performance was initially inhibited by the fact that half the Vietnamese troops were on Tet leave when the enemy struck, and many ARVN units gave a good account of themselves in the subsequent fighting. Press pronouncements that the offensive eroded loyalty to the GVN were ill-informed.

He goes on to discuss several flaws in the coverage. If you are asked to write how the media messed up in Vietnam, this is a must read book. The review is a pretty good summary of a few of the points made.