From Internet, Kevin Reed:
And just how did that term 'Blue Plate Special' come about? During the Depression, a manufacturer started making plates with separate sections for each part of a meal - like a frozen dinner tray - it seems that for whatever reason they were only available in the color blue. Because they were inexpensive and saved on dishwashing, diners began using them for their low priced daily specials.

(the last paragraph of a long article about dining cars.)