There's always more than can be said, but this post by /u/Bernardito may answer some of your questions.

I'll let others speak to the reality of the indiscipline, but I can speak to the causes. In short: morale.

In the 1971 Armed Forces Journal, Col. Robert D. Heinl, Jr explains the causes of the morale downturn from an officer's perspective:

"Intolerably clobbered and buffeted from without and within by social turbulence, pandemic drug addiction, race war, sedition, civilian scapegoatise, draftee recalcitrance and malevolence, barracks theft and common crime, unsupported in their travail by the general government, in Congress as well as the executive branch, distrusted, disliked, and often reviled by the public, the uniformed services today are places of agony for the loyal, silent professions who doggedly hang on and try to keep the ship afloat."

Try to imagine fighting a war with no front lines (WoT veterans will have no problem making this leap, I imagine), in truly miserable country, where any victory won is never secure because unless you stay and hold the ground, enemy forces can retake any objective after you've left. American warfighting was very much designed around the idea of lines of battle where, once secured, rear areas were safe, objectives were often not fought over again unless strategic shifts occurred, and you could more or less understand where the "front" was.

Vietnam really had none of that. The NLF guerillas and NVA had considerable tactical advantages in-country and often chose the point of initiation for contact. Read Blackhawk Down and get a sense for the importance of tactical initiative to US commanders, and then realize that rarely did American soldiers have that initiative in Vietnam. That means you're fighting ambush warfare in difficult terrain, against an enemy that hits and fades with relative ease. Please note that it's not like US forces weren't combat effective, they just had very little to show for it - Westmoreland's emphasis on reaching the "tipping point" where the battle of attrition would ideally reach a point where the NVA and NLF could not resupply their lost manpower meant that body counts were the primary way of indicating whether or not there was success in any given operation (this is mostly prior to the Tet Offensive). Instead of capturing and holding territory as proof of your soldiering merit, you're instead charged with counting the cost to the enemy as a way of proving to your commanding officers that you're winning the war. Grisly, no?

So, we have a tactical situation where you’re never in control, contact is initiated largely by ambush, fighting would often devolve into close quarters brawls (less so in the highlands, but jungle fighting is almost always a close-fought affair), casualties were high, the terrain and climate were miserable, and you can start to understand why unit cohesion and morale began to suffer. The inability for the higher-ups to understand the nature of the conflict and the grisly reliance on body counts as a measure of success further contributed to the morale downturn.

This is getting long-winded so I’ll skip over the situation on the homefront – someone else should pick up that gauntlet as it’s just as important – imagine facing everything outlined above, and being thought of as a monster by the people you’ve left behind. What grounds you, as a soldier, then?