It depends on which mode of operation you use with the AES cipher. For instance in CBC mode, if a bit is flipped in a block of ciphertext, the whole block becomes garbage when decrypted, and in the next block the corresponding bit of decrypted plaintext is inverted (which may or may not be a problem depending on what the plaintext is). The rest of the stream afterwards is unaffected.
The wiki article on the subject is a good primer. See: Block cipher mode of operation