'The Centers for Disease Control (CDC) report minor side effects from the MMR-V and MMR vaccines to include low-grade fever, injection site redness or rash, pain at the injection site, and facial swelling. Moderate side effects include a full body rash, temporary low platelet count, temporary stiffness and pain the joints and seizures, and seizures.  
MMR-V, however, has been noted to have a higher risk of seizures than separate administrations of MMR and varicella vaccines, especially when given as the first dose of the series.
Rare serious side effects of both MMR-V and MMR include brain damage, coma, chronic seizure disorder, lowered level of consciousness and loss of hearing. 
Serious complications reported by Merck in the ProQuad (MMR-V) product insert during vaccine post-marketing surveillance include:
- atypical measles;
- vaccine strain varicella;
- varicella-like rash;
- herpes zoster;
- herpes simplex;
- pneumonia and respiratory infection;
- skin infection;
- subacute sclerosing panencephalitis;
- aseptic meningitis;
- aplastic anemia (anemia due to the bone marrow’s inability to produce platelets, red and white blood cells);
- lymphadenitis (inflammation of the lymph nodes);
- anaphylaxis including related symptoms of peripheral, angioneurotic and facial emema;
- ocular palsies;
- necrotizing retinitis (inflammation of the eye);
- nerve deafness;
- optic and retrobulbar neuritis (inflammation of the optic nerve);
- Bell’s palsy (sudden but temporary weakness of one half of the face);
- cerebrovascular accident (stroke);
- acute disseminated encephalomyelitis;
- measles inclusion body encephalitis;
- transverse myelitis;
- Guillain-Barré syndrome;
- syncope (fainting);
- febrile seizure;
- afebrile seizures or convulsions;
- polyneuropathy (dysfunction of numerous peripheral nerves of the body);
- Stevens-Johnson syndrome;
- Henoch-Schönlein purpura;
- acute hemorrhagic edema of infancy;
- erythema multiforme;
A 2014 published study on the MMR-V vaccine in Canada determined that the risk of febrile seizures to be double in children receiving the MMR-V vaccine when compared to those receiving the MMR and varicella vaccines separately.
A 2015 meta-analysis found a two-fold increase in febrile seizures between 5 and 12 days or 7 and 10 days following MMR-V vaccination in children between the ages of 10 and 24 months.
MMR-V vaccine contains albumin, a human blood derivative, and as a result, a theoretical risk of contamination with Creutzfeldt-Jakob disease (CJD) exists.
Merck states that no cases of transmission of CJD or other viral diseases have been identified and virus pools, cells, bovine serum, and human albumin used in vaccine manufacturing are all tested to assure the final product is free of potentially harmful agents.'
Read more: Side Effects of the Measles Vaccine Include Brain Damage and Death