It is common for cats, especially young kittens, to be slightly off colour for one or two days following vaccination and occasionally individuals will be a little tender at the site of the injection.
There is some concern that vaccinations could harm the immune system and cause immune mediated disease; this is disease caused when the immune system mistakenly sees healthy body tissue as foreign and attacks it. Evidence for this is purely anecdotal and there is no proof that vaccination causes these diseases. It is important to remember that significant complications following vaccination are extremely rare, and the risk of serious illness and death is much higher from the infectious disease that the vaccines protect against.