I see blank thumbnails, if you had them off then there woudl be no thumbnails, so guessing you have a redraw problem on the thumbnmails..
Try playing with these settings from your layers palettete flyout >> panel options. Enable top level only, or turn off layers entirely and see what happens.
Illustrator is pretty fast for drawign thumbnails for layers, so you may have a corrupt object in the document, or font issue.
Played around with these settings. They worked as anticipated but the thumbnails did not reappear even as they were turned on and off.
It must be a corrupt object although the poster is entirely composed of vector drawings taken from another illustrator file which is not experiencing any problems. I'll start rebuilding the poster in a new file and see how that goes.
I followed troubleshooting steps 3 and 4. With 4 I was able to retain the layer work I had done. Some elements which were locked (and I was unable to unlock in the corrupt file) were lost. But not too much additional work required to get back to my starting point.