I like your jokes. Here are some suggestions of improvement.
The Introduction is perfect. I liked the humor and the idea that you make the reader confused is completely relevant, if he didn't want to be confused, he shouldn't have typed "Quadruple Agent" on Uncyclopedia. However, make sure that your sentence actually makes sense, I am not even trying to understand it but some people will and will be upset if they understand that there is a logical mistake there.
Some information about the Middle Ages would be funny. For example, you can tell that in the Middle Ages quadruple agents were rather common but their concept changed. They were not the agents working for two camps (falsely, falsely, falsely and truly) but were working for a lot of camps at the same time and were quadruple only if working for 4 different masters (if you get what I mean).
Renaissance: they abandoned the medieval traditions and resurrected the previous idea: working for the first camp but spying falsely for the second one in order to falsely transfer information for the original one, etc. I don't know if you can find any examples of people who can be described as such.
Quadruple agents in art: as famous artists are often great artists, some great jokes can be made on this subject. This may also be connected to Renaissance above.
World War Two introduction is fine but you can add more there. Tell about how all the agents helped to win the war and maybe make a joke on German spies who were confused themselves, when being quadruple agents, and actually helped their enemy.
Dušan "Duško" Popov, one of the World War Two (double or more, his story is confusing) agent. Read something about him and he will be a nice (real) example.
Cold War just needs some examples and the intro can blame the q. agents for the fall of the USSR.
Good overall but needs more separate jokes than just the one which is confusing the reader.
Several completely new ideas I may suggest:
Becoming a quadruple agent + their education
Different intelligences that have such agents right now
Prose and formatting:
No improvements here except for links to other articles which you desperately need.
Several images can be added. I know that you didn't do it as you don't know which ones to choose, so here is what I can suggest.
Good article and I liked reading what you already have but more different topics should be raised up there.
A very good contribution, I hope my review will help you to keep going! Final score is out of 40.