Yes, the mimized window is a symptom. To go into a little more detail, the actual window becomes frozen and can be transparent. Clicking the program in the task bar does nothing. To users, the status does not change and messages are not received. Like Jason mentioned, the memory goes to 300MB when normally it's 100MB.
I have a machine that hibernates every night and has not been exhibiting the problem. The sleep case you bring up is interesting. It's easier for me to place a group policy making everyone sleep their machine than to reboot. Please let me know your results. Thanks!