I was thinking in the right direction, but with woefully incomplete information.
It turns out that modern MRI machines detect different phases (known as T1 and T2) of the nuclei recovering from the magnetic fields, and those recovery profiles do depend on the chemical environment (for instance, hydrogen nuclei in water recover differently than those in fats). This information yields much more detailed information that just distribution of hydrogen density. And it turns out that gadolinium has a paramagnetic effect that also affects the T1 and T2 timings of nearby hydrogen nuclei. I'm familiar with magnetism and even diamagnetism, but I knew little about paramagnetism. There is a hilarious (but quite wrong) description of how it works by heating up in the magnetic field on this page of the normally informative about.com, which also includes incorrect details about NSF/NFD incidence (see below).
Gadolinium itself, while not radioactive, is highly toxic, so it is bound up ("chelated") in a large organic molecule that tends to collect in abnormal tissue, making such areas easy to pick out. The large odd molecule is rapidly removed from the bloodstream by the kidneys. Unfortunately, for reasons that are not well understood, people with renal issues can suffer a horrible, untreatable, irreversible, fatal side effect: Nephrogenic Systemic Fibrosis or Nephrogenic Fibrosing Dermopathy. Victims suffer hardened, thickened skin which impairs mobility, muscle pain, yellow growths on the eyes, and kidney failure. In a couple of cases, the symptoms were reversed by kidney transplant. As the evidence mounted, the FDA required the gadolinium contrast vendors to include a boxed warning on the label (the FDA's strongest warning), and issued severely worded instructions to avoid "off-label" use (it had been used in a Magnetic Resonance Angiography, even though this was not an approved use, and the dosage used is much higher than for MRI). For some sobering reading (including some impressively foreboding molecular diagrams), you can read the labels on the FDA's site. I just had a look, and the new labels explictly state "NOT FOR INTRATHECAL USE" (the aforementioned off-label MRA use). I wryly notice on The GE Healthcare site that they still claim "proven safe and effective" (along with a footnote that is never expanded).
As the disease can be caused by a single dose of gadolinium contrast dye, in a person with only slight renal insufficiency (I already have kidney issues), I will in the future not consent to use of this drug until and unless the mechanisms are understood and a demonstrated safe formulation (in my sole opinion) is employed. New (non-gadolinium based) contrast agents (such as MS-325 and Combidex) are under development.