my $x = <$f>;
$! and croak "can't read mydata.txt: $!";
This is incorrect, since Perl does not guarantee that $! is cleared on a successful read. You'll have to check for errors by checking the return value of readline:
open my $fh, '<', 'mydata.txt' or die $!;
defined( my $data = do { local $/; <$fh> } ) or die $!;
close $fh or die $!;
But may I ask why you need this level of error checking? Are you reading from some kind of network resource for example? Because if it's just a regular file from a local harddisk, failures on e.g. close are pretty rare.
If you really do need this level of security, then one possible solution is using read and making sure the number of bytes read matches the file size - however, the following makes sense only if this is a plain ASCII or binary file, the file is not too huge, and note that the following has a theoretical race condition if someone else happens to be writing to the file at the same time as you're reading from it:
open my $fh, '<:raw', 'mydata.txt' or die $!;
my $size = -s $fh;
read($fh, my $data, $size) == $size or die $!;
close $fh or die $!;