First Two Weeks of October
The first two weeks of October, see daytime temperatures of mid 20's. The sun is now lower in the sky making crystal clear, light blue skies with warming rays. Rain is of course a possibility this late into the season. Evenings will feel cool and require a jumper - especially if you have spent the day sunbathing on the beach. The sea is still sufficiently warm for swimming - having had all summer to warm up, it takes several months to cool down. The landscape returns to its lush green state after the punishing summer.
Second Two Weeks of October
The second two weeks of October see daytime temperatures of low 20's. Beaches are deserted, and many tavernas and bars start to close. (Taverna Agni usually stays open till the end of the month though during the daytime - but is closed for the evening). Evenings can be cold and only the hardy will eat outside after the sun has set at about 6pm.
October does see some rain, usually only a few days worth per month though. Choose your accommodation carefully to ensure it is warm during the night and has somewhere to sit should it rain.
For me, October can be one of Corfu's finest months. The beaches deserted. Tavernas quiet and clear days with stunning views. (During the peak summer months, the humidity often makes visibility poor - sometimes completely obscuring the views of Albania from the Taverna). As an added bonus, flights and villa prices much lower. If you are prepared to risk the chance of rain, October should be an option for you to consider.