First, the operator to bind a regex match to a variable is =~ and to negate that, it's !~

Second, the operator to compare strings is eq. = is the assignment operator.

Now that that's out of the way, you could do something like:

if ( ($contents ne "") && ($contents !~ /^[\w \.\,\=\" \/<>]+$/) ){
    $contentserror = "Error - message.";++$error;
}
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This will first check if $contents is not empty, and if it's not, then check it against the regex, and if the regex doesn't match, then execute the body of the if statement.