See two screensavers when screensaver running

When my MacBook first displays its screensaver, it works just fine. After a few minutes, however, my screensaver begins to flicker back and forth between the original screensaver and a new running instance of the screensaver.

Very rarely, when I jiggle the mouse to bring up my unlock screen, the screensaver will still run behind the password box. In these instances, I have to type my password twice -- once into the original password box and one more time into another password box.

This is slightly annoying and I wonder if it is a symptom of a deeper problem.