Kefalonia has very little crime, although be careful in busy areas as most petty crime is the cause of tourists. Traffic, as everywhere in Greece, can be a little mad in towns. Out in the hills, the roads wind precariously around the sides of mountains. Some are passable only with a good 4 X 4, though the main routes are fine.
Watch uneven pavements in dimly lit streets.
The local police have a very low key presence and generally confine themselves to issuing speeding tickets and being suspicious of Albanians. You'll need a rep or interpreter if dealing with them for an insurance claim.
Mosquitoes are a minor issue in inland accommodation, less so by the beaches.
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A sizeable percentage of the local summer population live abroad in the winter months - there is simply not enough work on the island out of season Nov - April. Hence the large number of Greeks with American accents on the island. English is understood almost universally, with only senior citizens confined to their native language. Italian is widely recognised, due to the island's strong historical links with that nation. Venture a greeting in Greek anywhere on the island and you will get a warmly enthusiastic response.