It's not plausible in a US hospital for an intern to be there in the operating room without supervision. That is called "Shadow surgery" and is illegal.
A procedure at the bedside is a different story, like placing a central venous catheter. He could drop a lung (pneumothorax) and not realize it, not do a Chest X-Ray, misread the X-Ray, etc. Having the patient be a kid however makes it more difficult because there are regulations as to how high the staff to patient ratio must be at all times. If it has to be a kid.......mmmm.....misplacing the kid who is sick and therefore deprived of life saving care would be the most plausible. For instance, he misreads the kid's arm band, and basically sees the wrong kid, it's a busy night in the ER and he tells the head nurse to discharge the kid in bed 10 and follow up in the clinic on tuesday.
I've seen non lethal results of this happen when those in the medical profession fail to use the patient's name and instead say things like, "Go see the gall Bladder in bed 6"
Addendum: I thought of a scenario where it might happen in the OR. The attending or the attending surgeon designee (like an upper level resident) is supposed to be there from the time of incision until the time the patient is removed from the operating table. I have known some surgeons who were lax about it and might let the intern "close" unsupervised after the "case" was finished. In laparoscopic surgery, that means pulling out the scopes, checking for bleeding and putting in a few stitches. Historically it has happened that there was bleeding from a muscle at the time of the trochar assisted scope placement, but was unrecognized initially because the scope was putting enough pressure on the vessel during the surgery such that it didn't visibly bleed until the scope and operating ports were removed. If the intern failed to watch through the scope at the time of instrument removal, (s)he might miss that there was a bleeder. Bleeding follows the path of least resistance. If there is a hole in the abdominal wall fascia connecting to the abdomen, an abdominal wall muscle bleeder can bleed into the abdomen rather than appearing on the oputside as a hematoma. All that might be noticed is pain (which is expected after surgery) and then a few hours later the heart rate starts to climb from hypovolemia, but the intern thinks it's from pain and gives the kid pain meds instead of IV fluid and blood. About an hour later the patient's blood pressure suddenly falls and then a code is called.
Another scenario would be, the attending leaves, the intern starts to close and then the nurse say's, "there's a lap pad (surgical towel) missing from the count."
The intern doesn't want to reopen the half closed wound so (s)he feels around, finds it and pulls it out triumphantly and finishes closing, without remembering that that pad had been placed there as a means of putting pressure on bleeding from a raw area early on in the case and they all forgot to go back and check the area to find the bleeder.
In the intern's defense: the attending is supposed to be there, so it's never going to truly be only the intern's fault unless the intern is doing something without the attending's knowledge, but then the anaesthesiologist is going to say, "Where's the attending?" The only way around that I can think of would be if the case is over, the attending tells the intern to close, but after the attending leaves, the intern takes a look around and decides to cauterize a minor oozing from something which turns out to be a major artery. 1-2 days later the inflammatory effect from the cautery clots off the artery resulting in a dead organ and then another 1-2 days later, multisystem organ failure from disseminated intravascular coagulation (DIC). At the autopsy, (which would be mandatory) the pathologist would find the damaged artery and the attending would realize that (s)he had deliberately left that area alone, knowing the oozing was minor and would have stopped on its own. The intern should not have gone back in and started cauterizing things, but also the attending should not have left the intern alone and allowed such a thing to take place.