Try this:

<script language="Javascript 1.2">
function frmNewMember_Validator(form){ 
    if (form.Mem_Name.value == ""){ 
        alert("Please Fill in the Member Name field");
        form.Mem_Name.focus() ;
        return false; 
    }
    if(form.cboRegion.value == "None"){
        alert("Please Fill in the Region field");
        form.cboRegion.focus();
        return false;
    }
    if(form.Mem_Phone.value == ""){
        alert("Please enter your phone number in this format:\n222-222-
2222.");
        form.Mem_Phone.focus();
        return false;
    }else{
        var str = form.Mem_Phone.value;        
        var re = /^([0-9]{3}\-){2}[0-9]{4}$/;
        if (re.test(str)){
            return true;
        }else{
            alert("" + str + " is an invalid phone number!");
            form.Mem_Phone.focus();
            return false;
        }
    }
    return false;
}
</script>

From your original:

if (form.Mem_Phone.value<>"")
should use != (<> is vbscript isn't it?)

form.Mem_Phone.select();
?????????

and I think you got the last part a little muddled up. Hope this works (I 
haven't tested it).