Why does the slide sometimes lock open prematurely with rounds still in the magazine, or fails to lock open when the magazine is empty?

The slide not locking open on the last round is typically caused by the operator placing their thumb on the slide catch lever. This same operator error can also cause the slide to lock open during firing with rounds still in magazine.

Another possible cause is the incorrect assembly of the slide stop lever, specifically in how it engages the slide stop lever spring. Early Sig Pros had slide stop lever springs that were straight in the rear (that is, pointed rearward), shown on the left, but the current ones have "fool proof" slide stop lever springs that point downward where they engage the slide stop lever, shown on the right, and are thus not prone to incorrect assembly (photos are courtesy of Cliff Saunders):

If you have an older-style slide stop lever spring and inadvertently install the slide stop lever incorrectly, Sig-Sauer recommends that the spring be replaced.

Also note the different style of the decocking lever pad. The latest style is the one in the photo on the right.