After checking all the settings I had determined everything was set up as it should be and the most likely issue was the service provider they were using. They'd recently switched to this very well known international web mail service provider and since then emails were not arriving as expected.
The previous service provider was Bigpond which had an issue the previous consultant was not able to fix. I investigated this problem and found a way to work around the Bigpond issue. My experience with Bigpond is getting an issue fixed was unlikely to happen easily and this had already been attempted by the previous consultant. My testing showed Bigpond has an issue receiving emails to a particular account.
With everything now set up and working as expected, an email arrived on the client's iPhone with the message shown above. I'd received the same message and the example above is from my iPhone.
First the subject of the email with "S.x sells" didn't make sense, but the message "Email not displaying correctly? View it in your browser." made the client quite concerned and they thought things were again not working.
I showed the client the error wasn't an error and we can all learn something from this. The first line of the email is "Email not displaying correctly? View it in your browser.". This is because the email is formatted as a web page and should it not display correctly, the user will know what to do. However the first line is also the first line displayed in the limited summary area of an email which caused confusion. Making this informational message the second line of text and not the first could provide a more informative summary for the user and certainly give them less grief. The "S.x sells" made the email even more obscure, perhaps even suspicious and that obscurity is something that should be avoided.
If you're sending out emails to clients you now need to consider many will be receiving your emails on their mobile devices. The first line of text becomes very important. With smart phone usage increasing, you should consider the first line of the email as an important piece of information and not use it as a generic informational message.