One point that should not go unmentioned is that what former President Clinton is described as doing in that Times article is little different from what the first President Bush has done in his post-presidency. And his son is the president. So if it would be a problem with Bill, and I think it would be, it unquestionably is already a problem with the current president's dad. And no one has seemed to much bother about it.
Well, yes and no. The elder Bush's post-presidential influence-peddling may be as bad--or worse--than Bill Clinton's. But the situation is hardly analogous. To put it bluntly: George H. W. Bush doesn't live in the White House. He's not his son's principal adviser or surrogate, and certainly not half of the kind of two-for-one deal that Hillary and Bill seem increasingly to offer. Indeed, where Hillary's run is being framed explicitly as a Clinton restoration, W.'s campaign was framed as a rebuke to his dad's presidency, as his subsequent approach to social, economic, and (especially) foreign-policy issues aptly demonstrated. So while there may be similarities, it's hardly the same thing.
Update: Josh agrees, and amended his post accordingly.