This means we need to hire better contractors and hire managers who have technical background and require an audit periodically.
Open sourcing does not solve these two issues. healthcare.gov is not Django project. You can't install that system and the code is going to be big few people will be able to do anything about it. Plus, even if you could read the entire source code, accepting pull request, going through 3rd party security validation is going to take a while and people are probably not going to take your pull request.
What we need is to put the incompetent people out of job and hire good one.