I'll try to handle this as fairly as I can, and there are a few issues:
What's the relevant difference between a 527 and a PAC?
Technically, all PACs are 527s, but not all 527s are PACs. Section 527 is the IRS designation for tax-exempt political organizations, but only PACs can advocate directly on behalf of federal candidates. With that power comes heightened responsibility -- PACs may receive up to $5,000 each from individuals, other PACs and party committees per year, must register with the FEC and provide regular contribution and disclosure reports, etc.
527s are allowed to do "issue advocacy" only, and can do so with unlimited funds from individuals, corporations, PACS, wherever. You can see the current funders for the Alliance for New America via this link -- it's mix of local SEIU and other labor PACs, wealthy individuals writing five-figure checks and a check for $495,000 from "Oak Spring Farms LLC", which has been linked to the heirs of industrialist Andrew Mellon (including Rachel Lambert Mellon, who is 97 years old) and has supported pro-Edwards 527s in the past.
What's the big problem?
The big problem is that when a 527 does candidate advocacy, not issue advocacy, it needs to register as a PAC, and when it doesn't it will get fined by the Federal Election Commission (albeit years later), big-time. The links below will send you to the press releases announcing high-six figure fines against the most prominent 527s of the 2004 cycle:
Media Fund
Americans Coming Together
League of Conservation Voters 527 and 527II, MoveOn.org Voter Fund, and Swiftboat Veterans and POWs for Truth
As my frenemies put it today:
[T]wo campaign-finance advocacy groups -— Democracy 21 and the Campaign Legal Center -- argue that the Alliance for a New America may be violating other campaign finance rules. An Oct. 8 e-mail message circulated between union officials that was leaked through a rival campaign and published online by The New York Times suggests that the union officials planned to create the Alliance for a New America explicitly to advocate the Mr. Edwards election. (The group’s direct mail and television and radio commercials indeed strongly support Edwards, and its main staff worked for Mr. Edwards’s 2004 Democratic primary campaign.) Such advocacy of a candidate’s election could mean that the group falls under the restrictions governing so-called federal political committee rather than the looser rules applies to 527 groups; as a political committee, it could not accept contributions of union dues or other unlimited donations as it has. The Federal Election Commission fined several groups for violating the rules in similar ways in 2004.
"The SEIU memo raises serious questions about whether this 527 group is engaging in illegal activities," said Fred Wertheimer, founder of Democracy 21, including "whether this 527 group has failed to properly register as a federal political committee and to comply with the contribution limits and prohibitions that apply to the funds such a political committee can receive."
Paul Ryan, a lawyer for the Campaign Legal Center, said, "They may simply another in long line of 527 groups that simply ignore campaign finance law, and it may be doing so with a plan to pay a fine to the FEC."
And, indeed, that email is pretty explicit that the point of the 527 is to advocate for Edwards, not any particular issue, and I believe the ad itself is pretty clearly based on the candidate, not an issue.
To be clear: this is a legal issue for the 527 itself, not the Edwards campaign.
What's the coordination issue?
A federal candidate can't coordinate with a 527. That two former Edwards staffers work for the 527 does not prove coordination, nor does that email by itself. An FEC spokesman put it like this:
[A]ccording to Bob Biersack, a spokesman at the FEC, it would venture on the illegal if a candidate were to "coordinate" with a 527. Coordinate, according to the law, is defined as "in cooperation, consultation or concert with, or at the request or suggestion of, a candidate, a candidate's authorized committee, or a political party committee."
That said, Biersack adds, "as long as the decision to continue or stop was made by the group, then candidates are free to speak as to what the group is doing or what they hope the group will do. That would not in and of itself be coordination either." So Edwards could say, publicly, that he didn't want the 527 to run the ads (which he technically has) and Baldick, whose firm was on the Edward's payroll as recently as the campaign's second quarter, could call them off (which he hasn't).
If coordination were proven, it would be a problem for both the 527 and the candidate. That said, the FEC found no coordination in any of the cases above, though it was alleged in many of the complaints.
Finally, of course, since there's no FEC once this year ends, it's not like anything but post-hoc fines are going to happen no matter what.
I hope you found this helpful. I've tried to keep it as to-the-law and unbiased as possible; if there are errors, I will correct.
update: The SEIU has issued a statement denying that anyone did anything wrong.