I'm not 100% about the intricacies of how DNS works but is there no way for them to automatically mirror your DNS settings? That would make this process much much easier.
Yeah, a simple check to see what nameservers the domain is currently using and then warning about the possible downtime and offering to switch ahead of the transfer would have been a huge win.
I guess not because one of their steps is "Copy all your domain settings (host records, email settings etc) to our control panel." - who has time for that? :)