There is a checkbox on the plugin settings (Dashboard > Settings > Email Users) to enable debug mode. It is a setting you don’t want to leave on permanently as it attempts to intercept email as WordPress processes it and before it hands it off to the underlying OS mail transport.
When enabled, you do the normal “Send to Users”, “Send to Group” or “Notify Users” operation like you would during normal operation. When you press the Send button the Dashboard will update as normal but in addition to seeing the normal Dashboard content, the mail header information Email Users constructs will be output as well. It is is dumped in the format PHP stores it, the output isn’t fancy or well formatted but it does allow you to see the content of the mail headers as things like “TO”, “CC”, “BCC” and a few others will be the array keys in the information dumped out.
What you are looking for is to see if the content of the headers matches what you would expect to see for your target recipients. I recommend starting simple, pick 2-3 recipients as picking a group with hundreds of users in it can be overwhelming. By limiting it to a few users you can easily see the email addresses in the header to make sure they are formatted as expected and more importantly, all of the addresses you expect are included.
You should see the bulk of the addresses in the BCC field as that is what Email Users uses to send to more than one user at a time. If you pick a single recipient you should see their address in the TO field. The TO field will likely have the address for the admin user in it and the CC field will usually have the email address of the user sending the message.
If that all looks correct then I am not sure where to go next. wp_mail() is the WordPress API function which is used by WordPress itself to send email and Email Users uses it the same way.
Some hosting providers have rules about numbers of recipients in a BCC field which is why the BCC limit setting was added. Some hosting providers have other rules – it really varies so it is hard to know exactly what might be the issue.
Make sure you turn off debug when you are done.