Open the core/version file, what does that say?
The other files... try using a different FTP client. Are you using Filezille? I've always had bad luck with that. Some clients won't really re-upload the file if it sees the file is there already, or it doesn't overwrite it properly.
I use WinSCP and transfer using SCP or SFTP - those ensure that files are transferred across the line with integrity intact (by nature of the protocol), unlike FTP which just throws it over not caring if anything gets mangled in the process. The checkinstall.php is just a place to get started from (like in your case most of those errors went away), but if things are working right and it still shows errors, I wouldn't go crazy over it