The crime rate in island Greece is very low. The main rules for tourists are not to leave expensive things unattended, keep an eye on your wallet and change currency only in banks and official exchange offices.
The peak tourist season (July and August) is also the hottest time of the year in Kos. To avoid overheating, during the hottest hours (approximately from 13:00 to 16:00) it is better to stay in the shade or stay in your room and drink more water.
At the beginning and end of summer, evenings can be very hot and there is a danger of catching a cold. Of course, it is better not to go to the beach without sunscreen - the most "gentle" sun in Kos in May-June. In addition, you can step on a sea urchin or a stingray near the shore, and in September-October in the waters of the Aegean Sea there are a lot of jellyfish (do not take them in your hands, they can burn).
In April-May, pine trees and some cereals bloom in the area - if you suffer from allergies, be sure to bring antihistamines.