Chemicals peels can be very safe if done in the right hands. Sometimes even with the best conditions complications are always possible. Things that can happen include scarring, post procedure darkness, increased pigmenation (hyperpigmentation), decreased pigmentation (hypopigmentation), increased acne, and infections are among the things that can happen. A lot of this depends on how agressive you are.
The more aggressive you approach your wrinkles many times the better results but the flip side is that you have a greater chance of complications. For fine lines a less aggressive chemical peel can help and my choice is tricholoroacetic acid 10-20%. You can also consider retin A for fine wrinkles as part of your regular skin care regime. Laser resurfacing is another option as well, on more lighter settings and even the new technology of active fx fractional laser resurfacing with less downtime can be a newer alternative.
One thing to consider under the eyes is that the skin is a lot thinner and sometimes you have to be less aggressive in this area to avoid problems.