How do you transfer files to the system?

Answer

1.  This might seem minor, but how a company moves files around says a lot about their workflow and astuteness.
2. We use SSH/shell access. This is ideal. This is the most secure way to interact with a system. This means they're comfortable using command line. If they use a version control system and they're not using this... they're not using a version control system for the deploy.
3. We use a deployment tool to stage and deploy sites. This is better than the above option. This is more enterprise, so it's a really good sign. It's also more expensive in general; to do this correctly you can expect to pay $200-$400 a month in hosting alone. (Having said that, we use some of these tools, and we consider it development overhead—so we don't pass this cost along to our clients.)

We use FTP. This is a bad sign. There's nothing inherently wrong with FTP, but to use it for a deployment workflow leaves a lot of room for error. Given the risks involved, any developer using it is either inexperienced or not familiar with SSH. There's also pretty serious security implications of using FTP; though these are mitigated by using SFTP.