527 organizations should not be eliminated.
Why you are right:1. They are not shadowy. The IRS now requires 527s to disclose "the names and addresses (and occupation and employer if an individual) of all persons who contribute $200 or more...and of all persons receiving expenditures of $500 or more." This information is searchable and publicly available. You can find it here. (IRS website)
2. If 527s were eliminated it would empower wealthy individuals over groups. The constitution prohibits limiting an individual's own political speech. (The government can constitutionally regulate individual contributions that finance other people's political speech). If 527s were eliminated it would simply provide an additional advantage for people who have enough resources to fund their own political speech relative to those of limited resources. (Buckley v. Valeo)
3. Political speech is a good thing. The effect of eliminating the 527 form would be to reduce to amount of political speech because it would be harder for people to organize. Political debate is at the center of any functioning democracy. It shouldn't be only available to political parties, candidates and the very wealthy.
Why they're wrong:
Calls by President Bush and others to eliminate 527s are simply a political ploy to avoid directly condemning advertisements by the Swift Boat Veterans for Truth. But the problem is not with 527s themselves. The problem is that the Swift Boat Veterans for Truth are lying.