Hope someone informed actually answers this interesting question.  I
believe PET scans can show inflammation, but they are more often used to
demonstrate tumors.
    But the presence of inflammatory change in an organ can often be
indirectly inferred from other tests--angiography, urinalysis,
colonoscopy etc.
    Obviously, biopsy is the gold standard if there is no other way.

Steve

Out of my expertise here as it would be something in radionucleotide
radiology department. The one most mentioned is gallium-67 citrate
which can be used to locate inflammation.

One has to distinguish inflammation based on the type of cells
associated with inflammation and the cytokines that promote their
distribution. Acute inflammation is best illustrated by sepsis or
infection and the cell associated with such acute infections is the
neutrophil. In contrast to acute is the chronic inflammation of
lymphocytes and monocytes.

http://www.patentstorm.us/patents/5811073-description.html

When speaking of autoimmune disease one is speaking about lymphocytic
infiltration into target organs. Generally the presence of autoimmune
antibodies directs the immune response and provides specificity. The
key is to find organ dysfunction and characterize that dysfunction as
immune in origin. Generally when an organ is affected by such
autoimmune attack the organ is affected. It may be specifically
located based on the organ or it may be diffuse based on the
distribution of the target tissue.

Medicine has always been symptom based and so the differential
diagnosis flows around that base. The flow involves the history,
physical examination and laboratory testing. It is not always
necessary to biopsy for some autoimmune diseases that are classically
defined by the above. Other disorders are not so well defined and
might rely on biopsy for proof. This usually happens with conditions
that may have ambiguous antibody testing. One then gets into sampling
adequacy of single biopsies or multiple biopsies etc.