Vaccines have side-effects
For accurate information on the efficiency of vaccines, consult the WHO website.
The oral polio vaccine can, on increably rare occasions, cause paralytic polio. Some flu inoculations can on occation cause Guillain-Barre syndrome, while others can lead to anaphylactic shock. These are all known and accepted side effects for vaccinations, they are however incredibly rare. Putting the benefits of the inoculation aside, it is impossible to argue that vaccines are “entirely safe” when these are possible side effects. However it should be noted that basically nothing is entirely safe. The chances of a "dose related incident" resulting from the first administration of polio vaccine is approximately 1 in 520,000. This puts your chances of developing symptoms it in a similar range of being struck by lightning in a given year. 
Side-effects are very rare and 90% of these are mild, usually limited to soreness and inflammation around the injection site. More serious side effects are exceptionally rare. Compared to the diseases prevented, any side-effects are minuscule: for example, Influenza vaccination has been shown to lead to a 1 or 2 per million people increase in Guillain-Barré syndrome, whereas having the influenza disease gives a much higher chance of developing Guillain-Barré syndrome. There is concern that the mutated version of polio that is contained in the vaccine can lead to polio. Since 2000, approximately 13 million cases of polio have been prevented compared to 760 cases from the mutated vaccine. Recent modifications of the vaccine have reduced the chances of disease from the mutated vaccine. There are fewer side effects of most vaccines than there are with paracetamol or acetaminophen.
[P1] Vaccines carry side effects that can be severe. [P2] Therefore, they are not safe.
Rejecting the premises
[Rejecting P1] These side effects are exceptionally rare. [Rejecting P2] Vaccines are safer than paracetamol and acetaminophen, products we typically think of as "safe". Therefore, vaccines are "safe".