Short version:
There were three big errors related to attempts to cut costs:
1. The M16 was designed to use a new extruded IMR powder. The rifle's timing was entirely based upon it. McNamara's bunch said, "We've got plenty of older powder sitting around. Use it!" The result was higher port pressures that led to faster expansion down the gas tube. The net result was that the bolt began to travel back while the spent casing was still obdurated, that is, swollen to seal within the chamber. Either the extractor would jump the rim of the case or tear it off, leaving the case wedged in the chamber, turning the rifle into a single shot weapon until each case was driven from the chamber.
2. The chamber was intended to be chrome-lined but that was cut as well, making friction higher and extraction tougher. After the powder problem was discovered it still had problems with extraction. Then this problem was discovered and the Army decided to go ahead and spring for chrome plating. However, they didn't bother to change the chamber spec to have it widened to allow the extra width chrome plating would add. Any benefit of plating was lost for a good while until this goof was figured out.
3. That new extruded IMR powder was supposed to be used was a pretty clean burning powder. So, soldiers were officially taught that this wonder weapon didn't need to be cleaned due to its wonder weapon status. That was unfortunate in that the M16 was the first U.S. Army weapon that "pooped where it fed," ie' the exhaust propellant gasses were vented right into the works of the weapon. Between not being cleaned and the use of regular, dirty ball powder, the M16 was the dirtiest weapon on the books at adoption.
And I haven't discussed light primers and heavy firing pins yet.
Bob