Adverse reactions to vaccines occur in cats (as they can in most animals). Side effects from vaccinations vary with the type of vaccine used, and the age and breed of the cat vaccinated. It is important to know the type of reaction that can occur, particularly if you give your kittens their vaccinations yourself.
One of the risks of showing cats that all exhibitors acknowledge is the possibility of their cat "catching" something from one of the other cats at the show. Most cat registries have enacted a 21 Day Rule as part of their show rules, meaning any cattery that has had an infectious problem must not enter ANY cats in a show for 21 days following the date the cattery has a clear bill of health.