Could it still be possible that some files would have gotten corrupted if they were interpreted as text and others were sent ok without being modified to text?

Yes, but it's unlikely. The difference between ascii and binary modes are that text mode will translate any CR/LF combinations to LFs only. So if a file had no CR/LFs in it, then it wouldn't have gotten corrupted, but that means that a mulitmegabyte file would have to never have those two characters together, which is unlikely.

could someone tell me how to force a binary transfer

It will depend on your client. It should be reasonably obvious if it's a GUI client. If it's a text client, try typing ``bin'' and see what it says.