The Linux Foundation handles the Linux kernel, so they have a good track record in that regard. They also have worked on some less-successful (but very well-managed) initiatives like Meego and now Tizen.
The members are big corporations and as a result, the auditing process and outlay of funds isn't something I'd be concerned with.
The greater (potential) concern would be over how the corporate sponsors could influence a project. Zemlin assured me that the SOP is not to interfere with existing operational structures or governances of a project -- so they wouldn't have any impact on how the OSF is run, for instance -- and certainly, in the case of the Linux kernel, corporate sponsorship hasn't dictated Linus's direction of the project.
That said, I think the level of influence a corporation could have over a project is probably directly related to how a project is initially structured. Tizen, as an example, is in partnership with the Linux Foundation, but is largely led by Samsung and Intel. That's totally fine, and was that way by design.
I would be concerned about projects that might not have strong leaders (like Linus). Of course, one could argue that if that's the case, the project might have bigger problems than being co-opted by other entities.