Don't forget to use strict; and use warnings; (or -w). Additionally, you may be interested in use diagnostics; which expounds upon perl's error messages, which returned (for the above code):

Bareword found where operator expected at ./tmp line 20, near "$%error_msgs" (#1)
    (S syntax) The Perl lexer knows whether to expect a term or an operator.
    If it sees what it knows to be a term when it was expecting to see an
    operator, it gives you this warning.  Usually it indicates that an
    operator or delimiter was omitted, such as a semicolon.


        (Missing operator before error_msgs?)
syntax error at ./tmp line 17, near ") )
                                           "
Global symbol "$error_msgs" requires explicit package name at ./tmp line 18.
syntax error at ./tmp line 22, near "}"
Execution of ./tmp aborted due to compilation errors (#2)
    (F) Probably means you had a syntax error.  Common reasons include:

        A keyword is misspelled.
        A semicolon is missing.
        A comma is missing.
        An opening or closing parenthesis is missing.
        An opening or closing brace is missing.
        A closing quote is missing.

    Often there will be another error message associated with the syntax
    error giving more information.  (Sometimes it helps to turn on -w.)
    The error message itself often tells you where it was in the line when
    it decided to give up.  Sometimes the actual error is several tokens
    before this, because Perl is good at understanding random input.
    Occasionally the line number may be misleading, and once in a blue moon
    the only way to figure out what's triggering the error is to call
    perl -c repeatedly, chopping away half the program each time to see
    if the error went away.  Sort of the cybernetic version of S<20
    questions>.

Uncaught exception from user code:
        syntax error at ./tmp line 17, near ") )
                                           "
Global symbol "$error_msgs" requires explicit package name at ./tmp line 18.
syntax error at ./tmp line 22, near "}"
Execution of ./tmp aborted due to compilation errors.

Additionally, remember that $name != $error_msgs{'name'}; I think you may be looking for something like:

my %errs = (
    name => 'Unspecified',
    email => 'Invalid'
);

my %fields = (
    name => 'Bob',
    email => undef
);

foreach (keys %fields) {
    print $errs{$_} unless $fields{$_};
}
[download]

Given the above implementation (in the OP code), you may also be interested in warn and die.