What is a Vaccine Adverse Reaction?
A vaccine adverse reaction is defined by The Merck Manual as having the same neurological complications as from a viral disease:

“Acute disseminated encephalomyelitis … is characterized by perivascular Cental Nervous System demyelination, which can occur spontaneously but usually follows a viral infection or viral vaccination (or, very rarely, bacterial vaccination), suggesting an immunologic cause. Acute inflammatory peripheral neuropathies that follow a viral vaccination or the guillain-barré syndrome … are similar demyelinating disorders with the same presumed immunopathogenesis, but they affect only peripheral structures.”

http://www.merck.com/pubs/mmanual/section14/chapter180/180a.htm

From The Encylopedia Brittanica:

“Encephalitis, plural Encephalitides, inflammation of the brain; from Greek enkephalos (“brain”) and itis (“inflammation”) … Encephalitis is most often caused by the direct or indirect action of an infective organism and sometimes by such noninfective agents as chemicals.

Although encephalitis can be produced by many different types of organisms, such as bacteria, protozoa, and helminths (worms), viruses are the most frequent causal agents.

Among children, a large number of acute encephalitides are of the type known as demyelinating encephalitis, which may develop as a complication of such viral diseases as measles or chicken pox OR AS A RESULT OF VACCINATION against such viral diseases as smallpox.  It is so-called because damage is not done to the nerve cell body but to the insulation (myelin sheath) surrounding the nerve fibers. Multiple sclerosis is the best known of another group of encephalitides in which there is injury to the myelin.

Among the chemicals that occasionally produce encephalitis are lead, arsenic, MERCURY, ethyl alcohol, chlorinated hydrocarbons, morphine, and barbiturates. Symptoms common to most types of encephalitis are: fever, headache, drowsiness, lethargy, coma, tremors, and a stiff neck and back. CONVULSIONS MAY OCCUR IN PATIENTS OF ANY AGE BUT ARE MOST COMMON IN INFANTS. Characteristic neurological signs include uncoordinated and involuntary movements, weakness of the arms, legs, or other portions of the body, or unusual sensitivity of the skin to various types of stimuli. The symptoms, signs, and an examination of the cerebrospinal fluid can usually establish the presence of encephalitis, but they do not necessarily establish the cause, which often remains unknown. This situation makes specific treatment difficult, and even when the causative virus is known, there may be no drugs effective against it …

The symptoms remaining after recovery from the acute phase of brain inflammation vary considerably, depending on the type of encephalitis and on the age and general health of the patient … ANY FORM OF ENCEPHALITIS IN YOUNG CHILDREN MAY DAMAGE THE BRAIN SO THAT IT CAN NO LONGER DEVELOP PROPERLY.”

http://www.britannica.com/bcom/eb/article/6/0,5716,33156+1,00.html

Note: Merck cautions that children with fluctuating or progressive neurologic disease should not be immunized until their condition has been stabilized for at least one year because of the risk of cerebral irritation … children with known or suspected immunodeficiency disease should not receive any live virus vaccines, since they could initiate a severe or fatal infection. Patients with either B or T cell immunodeficiencies should not be given live vaccines (e.g., measles, mumps, rubella, poliovirus, BCG) because of the risk of vaccine-induced illness, and family members should not receive live poliovirus vaccine.”