In answering this question, I have chosen to focus on a very common topic when talking about atrocities in the Vietnam War. The killing of unarmed civilians by gunners and/or soldiers on helicopters has long been associated with the topic of American atrocities in the Vietnam War. The iconic image of the UH-1 Bell "Huey" helicopter mixed in with the terrible revelations of war crimes in the Vietnam War has made this particular topic very potent in the popular imagination of the Vietnam War. This leads us to two questions: 1. Did anything like this actually take place during the war? 2. If so, how widespread/common was this?
The topic of atrocities in war is a sensitive one. This is particularly so when talking about a controversial conflict like the Vietnam War where a great deal of participants are still alive. Like the war itself, the topic of atrocities has been considered in a great many ways from different contemporary political perspectives. It is a misunderstood area of study that still produces a lot of controversy. One such case is the popular history book Kill Everything That Moves by author Nick Turse whose arguments have entered the mainstream but has been criticized by scholars of the war for being too generalizing and decontextualized. That is a challenge that meets any scholar dealing with Vietnam War atrocities and will be something that I will come back to in the second part of this answer. Another challenge that confronts us is: how do we know that an atrocity took place?
On July 1st 1969, the villages of Phu Vinh and Diem Pho in the Quang Tin Province were attacked by four helicopter gunships from from D Troop, 1st Squadron, 1st Cavalry Regiment of the 23rd (Americal) Division. Ten villagers were killed and fifteen were wounded. This attack had been committed with permission from higher command. Why? Because the men had claimed that they had been under attack. The dead and wounded were all civilians. The perpetrators would claim that they had been fired upon and that they had managed to blow up a weapons dump that were stored inside of the village. This could ultimately be debunked when no traces of ammunition or of the destroyed weapons dump could be found by a USMC CAP (Combined Action Platoon) that visited the village of Phu Vinh in the aftermath of the attack. The men had lied about being fired upon to gain permission to attack innocent civilians and afterwards lied to investigators. If the CAP hadn't visited Phu Vinh and therefore been able to refute all claims made by the perpeators, we probably wouldn't have been able to point this out as a confirmed atrocity.
This example of a contemporary investigation into an atrocity gives us some, albeit limited, insight into how an atrocity could be confirmed. Not all atrocities during the Vietnam War were as widely reported and investigated by American authorities like the infamous My Lai massacre. Nor are atrocities like those committed by Tiger Force of the 101st Airborne Division in 1967 as thoroughly investigated as they were by Michael Sallah and Mitch Weiss (for which they won a Pulitzer). During the war, the Criminal Investigation Division (CID) were responsible for investigating claims of atrocities. As historian Bernd Greiner shows in his book War Without Fronts: The USA in Vietnam (Vintage 2010), the CID appeared to be lacking interest in pursuing some actual credible leads into atrocities and in cases like the Tiger Force, the final report was delivered to the White House and became the target of a cover-up. The CID files are available to scholars today but they can be very frustrating. American soldiers could, for example, be very precise about time and place but would not to name perpetrators (which would have made things difficult for the CID). In Bernd's investigation, using files from the Peers Commission and the Vietnam War Crimes Working Group, we are left with around 246 allegations of atrocities that were considered credible by the two groups out of hundreds of files from the CID. The methodology behind choosing these 200 + cases is left unsaid and there are many limitations on using these accessible files, such as the fact that the majority of cases are drawn from the I and IV Corps Tactical Zones. Once more, the reasons why escapes us.
This goes to show how difficult it is to not only do research into a topic like this but how contemporary sources makes that even more difficult. I would recommend reading Greiner's book for a more extended and detailed explanation of his methodology and the source material available, as well as for his very scholarly approach to the topic. Seven massacres committed during the Vietnam War has been confirmed, with the most infamous one (My Lai as well as My Khe which happened simultaneously and is usually included with My Lai) resulting in 420 and 90 deaths respectively. The other 5 massacres resulted in around 100 deaths altogether. To these massacres, we can add individual cases like the case previously mentioned or the killing of prisoners of war by soldiers in the field. However, we do not have any estimations of how many civilians were killed by American soldiers, nor do we have any real ideas of how widespread this is. To be able to sufficiently answer the question of whether or not this was common is not possible considering the limited source material that we have. We are not able to independently confirm all these cases, although a thorough scholar focusing on particular incident might be able to do so by following the methodology that Sallah and Weiss used in their investigation on the Tiger Force.
Generalizing, like Turse has done, can therefore be very problematic. There are no indications that there was a widespread acceptance of atrocities or that they were actively encouraged, as shown by the cases (such as the one above) of soldiers lying to their superior officers so as to enable them to committ atrocities. However, scholars such as Greiner has argued that the body count system in which the quantity of dead enemy combatants became a way to measure victory actually became an indirect way of encouraging atrocities amongst some soldiers since they could easily just claim that the dead civilian they murdered was just another PLAF fighter - something which we have proof that soldiers did. More extreme claims, however, that the United States were committing genocide in the Vietnam War and that soldiers, officers and commanders on all levels explicitly set out to kill as many South Vietnamese as they could are false and contradicts actual evidence that we have available to us. Nonetheless, the evidence for the deaths of well over a thousand South Vietnamese civilians are well-documented in the investigations of the American government and relevant military authorities. This is not something that could or should be denied or overlooked.
As a follow up question is there any information about Vietnamese prisoners taken by the Americans?
Did they even take prisoners? There doesn't seem to be any information available on the topic.