I'd suggest something like the following:
Treat this like a software development project, except we're coming up with a government instead of a program.
1. Setup a public bugtracker, where people can submit examples of federal government acting incorrectly (attached to bugs, have relevant news articles, studies, and impacts for why it is important).
2. Setup a repo with a "blessed" version of the founding documents of the government. Anyone can read the docs, and suggest changes. Any changes to the laws would have an easy-to-follow path in the changelog, and linked tickets from the bug tracker demonstrating that they were necessary. These docs can be forked, but the blessed branch gets the "official" reference implementation.
We've had the tools to "fix" government for years now--we should start using them.
Things I'd personally like to see:
1. Who controls the "blessed" version? This is a hilariously interesting problem, and likely would end up with some kind of set of "core" developers. That said, we have the tech to make relatively authenticated, secure votes (PGP or somesuch). I'd suggest using that to accept changes to mainline, and if it becomes obvious the core devs aren't paying attention we fork. This might be really slow to get things accomplished (past the initial bootstrap), but that's okay in government--the more conservative your creation of policies, the better.
2. A creation of a structured query language for determining if an action obeys a law. This would be really tricky, but if the core docs can unambiguously be parsed and tested against so many problems in government simply go away. I don't really expect this to get done, but it's an intriguing idea, no?
3. My personal belief is that a good government is like a good operating system: it provides basic infrastructure when you need it, is invisible when you aren't looking for it, and protects you from other things in the environment (and them from you!). So, a lean, simple, easily-verifiable government that protects basic rights and provides basic needs and which only intervenes when processes (groups) come into direct conflict seems like the correct goal--not this bloated ill-defined overreaching contraption we have today.