If you use your fingers to apply a product from a jar, there is a small chance of introducing contamination over time that might overwhelm the preservative system and introduce bacteria or mold. That's a slim chance, and mitigated by making sure you don't let the product sit on your shelf too long. Be sure to pay attention to any Use-By/Expiration date or P.A.O. (Period After Opening) warning on the package.
An open jar is also more exposed to oxygen, and can affect antioxidants and other active ingredients and potentially make them less potent. Again, this side effect can be mitigated by making sure you keep the jar sealed, and use the product in a reasonable timeframe once opened.