As you would expect, alcohol is haram, and this is clearly established by the Qur'an and Sunnah.
As for what percentage, there is a hadith that says "what is haram in large quantities is haram in small quantities" But what about really, really small quantities?
Another hadith often used in tahara states that:
If the colour, smell, or taste changes, the purity changes.
This hadith is da'eef; however, by ijmaa, all of the scholars agree to the principle outlined in this hadith.
Based on this, many scholars say that, with food, some quanity of impurity is allowed, without changing the ruling on the food. How small a quantity?
One of my teachers said "I asked shaykh Ibn Uthaymeen this question, and he told me: shari'ah doesn't come with numbers."
You can read this long explanation about the halality of Doritos, which explains this issue in excruciating detail (among other issues). The shaykh suggests a number like 0.0001% of haram will not affect the final purity.
Source: Weekend class on fiqh of food and clothing