My wife had a C-section a month ago, then developed an infection because of leftover placenta pieces. How is this possible at a C-section where everything's so exposed?
At the time of a C-section, the inside of the uterus isn't examined completely. To do so would mean rearranging the surgical lighting in such a way that would unreasonably delay what would need to be done at the time—like sewing back up the uterine incision—which is bleeding profusely until done so. Most doctors will use a lap square (linen piece) to rub out any remaining pieces of placenta from within the uterus by inserting the lap square and a hand up into the uterus before closing it. This only takes a couple of seconds and will not unduly delay the progress of the surgery. So this is in effect a "blind" procedure, and everything is not so exposed as you would think.
Sometimes some membranes can be particularly adherent to the inside of the uterus and won't come very freely, even with this technique. Also, sometimes layers of placental tissue can even be growing into the muscle of the uterus, making separation impossible, and when no more placental tissue comes out with the lap square, it is assumed that all is out.
These are all outcomes that are merely bad luck and not negligence. And if these remnants remained after a C-section, then they probably would have remained after spontaneous expulsion of a placenta in a vaginal delivery as well.
Treated appropriately, this episode shouldn't interfere with any future pregnancies.