Are you looking for something like this?

use vars qw( $error );

sub do_lots {
    $error = 0;    # assume things are correct unless told otherwise
    my %hash = @_;
    %hash = mangle_once(%hash);
    return $error if $error;
    %hash = mangle_twice(%hash);
    return $error if $error;
    # ... as necessary
}
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That assumes the embedded subs set the global $error when there's a problem.

You could also return hash refs from your embedded subs, capture them in a temporary value, and check for definedness:

    my $result;
    $result = mangle_once(%hash);
    return $error unless defined $result;
    # et cetera
[download]

Returning either an error code or a flattened hash can be a little trickier, and I probably wouldn't do it as it would make the code less clear.