PHP Notice: Undefined index/variable, and invalid arguments, but form works

Question

I'm just trying to clean up these error logs. I have a form on my site, that WORKS. But my error logs are still showing the undefined indexes. I checked this question, PHP - Notice: Undefined index:, and I think it's what I need but I'm not sure how to implement it to stop sending errors. Again, the form does work, so then why am I getting these errors and how do I stop them.

Note*: If it's a duplicate then comment me, please don't mark it. I see this question as being different since it's not preventing my code from working. I just want to get rid of the errors because it makes no sense how the error code works.

Errors:

[14-Sep-2015 14:40:41 UTC] PHP Notice:  Undefined variable: MSG in /home/seenserv/public_html/contact.php on line 134
[14-Sep-2015 14:40:41 UTC] PHP Warning:  implode(): Invalid arguments passed in /home/seenserv/public_html/contact.php on line 47
[14-Sep-2015 14:40:41 UTC] PHP Notice:  Undefined index: name in /home/seenserv/public_html/contact.php on line 138
[14-Sep-2015 14:40:41 UTC] PHP Notice:  Undefined index: phone in /home/seenserv/public_html/contact.php on line 139
[14-Sep-2015 14:40:41 UTC] PHP Notice:  Undefined index: email in /home/seenserv/public_html/contact.php on line 140
[14-Sep-2015 14:40:41 UTC] PHP Notice:  Undefined index: invoice in /home/seenserv/public_html/contact.php on line 141
[14-Sep-2015 14:40:41 UTC] PHP Notice:  Undefined index: comments in /home/seenserv/public_html/contact.php on line 142

FORM:

<form method="post" action="">
                <input type="text" name="name" placeholder="&ast;Name" value="<?php echo $_POST['name']; ?>">
                <input type="tel" name="phone" placeholder="&ast;Phone Number" value="<?php echo $_POST['phone']; ?>">
                <input type="email" name="email" placeholder="&ast;Email" value="<?php echo $_POST['email']; ?>">
                <input type="text" name="invoice" placeholder="Invoice Number &lpar;optional&rpar;" value="<?php echo $_POST['invoice']; ?>">
                <textarea name="comments" maxlength="500" rows="10" cols="10" placeholder="&ast;Please enter your comments here..."><?php echo htmlentities($_POST['comments'], ENT_COMPAT,'ISO-8859-1', true);?></textarea>
                <button type="submit">Submit</button>
            </form> 

PHP Form functions:

    if(!array_filter($MSG)){
        if(!filter_var($email, FILTER_VALIDATE_EMAIL)){
            $MSG[] = "Invalid Email Format (test@provider.com)";
        }
        else{
            $POST['invoice'] = $invoice['invoice'];
            if(send_mail($POST)){
                header('Location: messageSent.php');
            }
            else{
                $MSG[] = "Email Failed. Please Try Again.";
            }
        }
    }
}

function filter_post($POST){
    $keys = array('name','phone','email','invoice','comments');
    $POST = array_intersect_key($POST, array_flip($keys));
    $POST = array_map('strip_tags', $POST);
    return($POST);
}

function check_empty($POST){
    foreach($POST as $key => $value){
        if(empty($value)){
            $MSG[] = "You need to fill out the $key section";
        }
    }
    return($MSG);
}
function send_mail($POST){
    extract($POST);
    $to = '7servicerepairs@gmail.com';
    $sbj = 'New Question For Se7en Service!';
    $msg = "Name: $name \n Phone: $phone \n Email: $email \n Invoice #: $invoice \n Comments: $comments";
    $headers = "From: Se7en Service Customer Care <7servicerepairs@gmail.com>\r\n";
    $headers .="Reply-To: $email";
    return(mail($to, $sbj, $msg, $headers));
}
function output_errors($MSG){
    return '<ul><li>' . implode('</li><li>', $MSG) . '</li></ul>';  
}
function test_input($data) {
   $data = trim($data);
   $data = stripslashes($data);
   $data = htmlspecialchars($data);
   return $data;
}
?>