Forms being submitted without required questions answered

I've had more than one form submitted without required questions having an answer entered.  Do I have do do anything else besides mark a questions as required in order to block the submit button until they are answered?

Is this the form you are having issues with http://www.jotform.us/form/60486053469159?

I have tested that form, but I was not able to replicate mentioned issue. I was not able to submit the form without filling all required fields. 

I have also inspected your form and your form has 22 input fields, however your email Notification has only 18 fields and values of those fields. Because of that you are not receiving all data inside of your email Notification. It seems that you have added new fields to your form and because you have edited your email Notification, new fields and values of those fields were not added to your email Notification. This means that all required fields were filled, only data from those fields is missing inside of your email Notification.

To resolve this issue I would suggest you to create new email Notification and delete old one. When you create new Notification all fields and values of those fields will be automatically added inside of your Email Notification.

https://www.jotform.com/help/25-Setting-Up-Email-Notifications 

http://www.jotform.com/help/132-How-to-Delete-Notifications-Autoresponder 

You can see previously submitted data on submission page of your form:

https://www.jotform.com/help/269-How-to-view-Submissions 

Hope this will help. Let us know if you need further assistance.

Thanks for the quick response.  That is the form that people have submitted without required fields filled in.  I'll make a new email notification.  Can you also test from where it is embedded on our website: http://bit.ly/23IHiAi 

I have just tried to submit a test form on your site, but every time I submitted a form leaving some require fields empty I got the warning message. It you still experience the problems please let us know. If possible please indicate the field(s) that is having issues.