They say you shouldn't proofread your own writing. Your mind has a tendency to read what you wanted to write instead of what is actually on the paper.
Similarly, you may be less likely to catch your own mistakes when testing your programming code. You know your way around the software, how it works and what you want it to do. You may only run it through the paces of the intended functionaity.
A 3rd party who is unfamiliar with the coding or intent of various functions within the program may be more likely to find flaws and weaknesses. They may try to use buttons or functions in ways not conceived of by the original author and discover vulnerabilities in the code that the original author may not detect.
For more information on Microsoft's proposal to use external patch "beta testers", see this article in The Register:Full Article