This was very common in early internet days, as FTP by default used 7 bit mode for transferring text, and you had to explicitly put it in binary mode for binary files (which of course you mostly forgot to do the first time).
But I can't believe both wget and ftp could be the culprits. Are there any firewalls/gateways upstream which could have been configured to strip the eighth bit - stopping people looking at pictures on the web maybe
Can you run a webserver? - if so you could wget from yourself and see if that works. Or can you swap the server for another machine and try that?