"Many eyes make all bugs shallow."
This is true, at least to an extent. The more people you have doing code review, the better your software will be (well, assuming that the people doing the review are competent and not, for example, Debian OpenSSL maintainers). This is true with proprietary and open source software.
"Open source means anyone can audit the source code and prove that the application is secure, bug free, etc."
If I'm using a piece of software and I decide I don't entirely trust it, I can pay people to audit it, as long as I have the code. I can pay companies like Coverity for their static analysis tools (actually, Coverity is free to use for open source projects), and I can fix any bugs that I find. If it's proprietary software, I can use some fuzzing tools and binary exploration to try to find bugs, but if I do find them then the license almost certainly doesn't allow me to fix them using binary patching, and doing so is a lot harder.
"Just open up your proprietary closed source code and developers will pop out of thin air to carry on development and fix all the bugs."
Fix all the bugs? No. Fix some of the bugs? Sure. If there are people for whom your software is valuable, then there are people who have a vested interest in improving it. If you can't persuade some of these to contribute to development, then you're doing something badly wrong.
"Launch an OSS project and a bunch of people will show up to help you build it."
I don't think anyone has ever said that with a straight face.
Apple is a company with a relatively small number of products, which rides a lot on the perception of their current flagship line. As such, a big part of the job for senior management is defining what the requirements are for the next iteration, balancing them with what's feasible, ensuring that they've done the market research to show that it will work, and then making damn sure that the product meets expectations.
The first serial (An Unearthly Child) survives and has been restored into pretty good condition. The second serial (The Daleks), also survives. The fourth serial (Marco Polo) is missing some episodes, and so are several of the later ones. Most of season 3 is lost (including all of four of the seven serials and most of several of them, such as The Daleks' Master Plan) and so are some important bits of Season 4 (including most of the last episode, when the first Doctor dies).
It's a very good argument for shorter copyright, as copyright holders apparently can't be trusted to ensure that our cultural legacy survives.
Perhaps it's different in other disciplines, but I've never seen an idea that could negatively affect my funding, and if there were one it would not be a dissident idea, quite the reverse. Grants aren't to prove that X is true, they are to explore the factors relating to X. If someone has an idea that is disruptive to an entire field (everything you were doing is wrong) then that produces more funding, not less, because now there are a whole new range of avenues of investigation. The things that negatively affect funding are (repeatable) results that show something so conclusively that there is no point in ever investigating it again, and those are very rare.
The AGW example is particularly silly, because fields where there is deep division in the scientific community are the ones where it is easiest to get funding, as everyone wants to know which competing theory is correct (or that they're both wrong). Most climate scientists I've met would love for there to be some strong, evidence-backed, scientific theories countering their work, because then their next grant application practically writes itself.
Well, one simple solution is multi-seat constituencies. This doesn't fix the issue, but it does make gerrymandering harder. You vote for (for example) two candidates, and the two candidates who get the most seats win. If the constituency is mostly Democrat, it will get two Democrats Representatives. If it's mostly Republican, it will get two Republican Representatives. If it's split down the middle, it will get one of each. The more seats per constituency, the harder gerrymandering is.
Another possibility is to have single-seat constituencies, but make them overlap, so that everybody gets to either vote for two or more candidates in different House elections, or (ideally) gets to choose which district they will vote in. This doesn't prevent gerrymandering, but it means that everyone can participate in it, rather than whichever party happened to be in power when they were moving electoral boundaries.
Of course, this doesn't help Republicans who are completely surrounded by Democrats or Democrats who are completely surrounded by Republicans, but hopefully that's a relatively small number, and not too unevenly balanced in either direction.
The real problem, however, is that the USA is a country of 320 million people using a political system that expects complete ideological agreement between most members. You need a system where no single party has close to a majority and so the Federal government has to operate by consensus, not by a small majority forcing its will over a slightly smaller minority. If you want an example of a good system of government to use in this situation, I'd recommend reading the Federalist Papers and the US Constitution...
To err is human, to moo bovine.