There are several problems with E10 (10% ethanol) gas in small engines:
1) The ethanol tends to attack rubber and some rubber-like compounds. Fuel lines, O-rings, and the diaphragm in the fuel pump were all effected by it. This was especially a problem with older saws. Newer saws tend to have newer rubber/plastic compounds which are more resistant to ethanol's effects. Unfortunately, many of them are not completely ethanol-proof, they are just ethanol resistant, so they still may break down over time. some of those affected parts are fairly easily replaceable with new, ethanol resistant parts (such as the fuel line). Others take a bit more doing (such as replacing parts during a card rebuild).
2) You should avoid using stale fuel in small engines. Since ethanol-blended gas is less stable than "pure" gas, it's even more important not to use old gas in small engines. This is especially important in 2-cycle engines, since the fuel is also their lubrication system, so the fuel gets into more areas of the engine than in a 4 cycle engine.
3) Ethanol is hygroscopic: it attracts and combines with water. It will actually pull moisture out of the air and combine with it. When E10 gas absorbs enough moisture, the ethanol/water mix will separate from the gas and sink to the bottom of the tank. This ethanol water mix is corrosive, and can do real damage if left in contact with metal parts. That ethanol is also now concentrated into a much smaller volume than it the 10% mix that was in the gas - so it will have even more effect on any rubber-type parts that are not ethanol-proof. It takes some time for a tank or can of fuel to pull enough moisture out of the air to cause phase separation. How much time varies depending on a lot of factors (humidity; how tightly sealed the tank is - most tanks are vented; how much airspace is in the tank - a full tank has less room for air, thus less opportunity to bring moisture in and less chance for condensation to form in the tank.
Some of these problems are lessened if you use the saw regularly and run it dry if it won't be used in the very near future. Some problems are at least partially helped by additives, but additives are definitely NOT a cure-all. As one additive manufacturer put it, "be careful not to buy into any false sense of security that a fuel additive is going to completely counter the harmful effects of ethanol, particularly when left in a tank for a long period of time." Some additives are more of a fuel system cleaner than a fuel stabilizer. Ethanol is an effective fuel system cleaner already, so if you are running E10 gas, there is little to be gained by adding a fuel system cleaner.
I had never heard the story Ruffdog mentioned about how adding 2 cycle oil lowers the octane rating of the fuel when added, so I can't comment about it's accuracy. I do know that the ethanol in E10 fuel adds about 2 points to the octane rating of the gas to which it is added. So if you get phase separation (as noted in #3 above), the remaining fuel is now 2 points lower (so if you started with 87 octane, you are at 85 octane after the ethanol separates out).
