Compiz and/or NVIDIA proprietary drivers are causing thick black border to be drawn around windows upon resume from sleep.
Workaround: Switch to a console and come back, i.e. CTRL-ALT-F1 followed by CTRL-ALT-F7. This forces Compiz to redraw the windows properly.
Of course, a normal consumer would not know this and would have to options, either suspend and resume again, hoping to solve the problem, or reboot the computer. Both cases are painful.
I upgraded the NVIDIA proprietary drivers to the latest version possible, since I have to use a legacy driver for my Lenovo W510. The problem still occurs with version 340.76-0ubuntu1~xedgers14.04.4.