The Libgcrypt library is fully thread-safe, where it makes sense to be thread-safe. Not thread-safe are some cryptographic functions that modify a certain context stored in handles. If the user really intents to use such functions from different threads on the same handle, he has to take care of the serialization of such functions himself. If not described otherwise, every function is thread-safe.
Libgcrypt depends on the library `libgpg-error', which contains common error handling related code for GnuPG components.