This piece is about the sovereign power of the King, or Queen since we have one of them right now. The purple is the indicator for this - purple being a very regal colour. The star and the yellow squiggles (technical term) are also demonstrations of the monarchs power - think of them as her knights, or maybe her black-clad army of freakin' ninja-assassin-robot-pirates.
The blue stretch is obviously the sea, with the lines over it representing the turbulent and stormy nature of well, the sea. But the major part of this piece is the words in the top left corner of the Art.
RICHARD NIXON IS A COMMUNIST.
Yes, when one thinks about it, it is should come naturally - he is a communist. A red. A pinko leftie. A, god forbid, a FREAKING SOCIALIST! This contrasts with the purple of the Queen - Whig and Torie (though American Whig for some reason) locked in an eternal epic struggle. Wrestling and fighting each other on some high summit in the mountains, like the kind Gandalf fought the Balrog on, or David Hume killed God upon.
Finally the "I like potatoes" part shows to demonstrate the pointlessness of these arguments. Since when it's all said in done, left or right, we all just want a potato.