Possible Arduino 1.0.1 Ethernet Library bug?

EDIT : If the socket limit were being exceed the message would be "Server not responding/busy"

Exactly! If that is not the case, then the challenge is elsewhere.

Then the WebInject program also shows errors when using the browser at the same time?

edit: You know that the web browser should be sending two GET requests, not just one. The first will be the webpage request, and the second will be for favicon.ico.

edit2: Have you tried to run two instances of WebInject?

I'll try to think of a way to test the sockets. If it is not using all 4, I would like to know why.

(moved this to post below)