The AFP over TCP: TCP error detection/correction has limits, so depending on your SNR, things can get pretty bad even with wired connections.
I was thinking on checksum, but the problem is that if you use the downloaded file to calculate the checksum, the file could already be corrupted and checksumming it would forward the error.
@carV3 is completely correct on the network side.
Messing up a few bits/bytes shouldn’t prevent the file from running (unless the header is corrupted, which is improbable due to the size difference between it and the data). It can definitely affect the audio, especially in compressed encoding. PCM/raw audio corruption should be less noticeable.
Edit: looks like, at least on SMB, a sha checksum can be used to guarantee integrity of the files if the client is configured to require the signature of exchanged messages (HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services\LanmanWorkstation\Parameters->RequireSecuritySignature=1). https://blogs.technet.microsoft.com/josebda/2010/12/01/the-basics-of-smb-signing-covering-both-smb1-and-smb2/
For samba (SMB for Linux/Mac), the equivalent setting in smb.conf seems to be client signing = mandatory . https://www.samba.org/samba/docs/current/man-html/smb.conf.5.html
NFS also has a similar setting, but requires both server and client to be properly configured with sec=krb5i option. https://access.redhat.com/documentation/en-us/red_hat_enterprise_linux/6/html/storage_administration_guide/s3-nfs-security-hosts-nfsv4
Couldn’t find anything similar for AFP, and since Apple deprecated it, I don’t think they will fix that.