These inconsistencies are most likely caused by your browser cache or “network cache” somewhere on the route to your site. Best is to start by refreshing the browser several times while holding Shift (Ctrl for IE/Edge).
If that doesn’t change the fonts, right-click on a paragraph in the editor and select “Inspect”. That will open the browser tools and clearly show you which styles are applied.
body#tinymce.mce-content-body {
font-family: Verdana,Arial,Helvetica,sans-serif !important ;
font-size: 12px !important;
}
The above code looks good, however these styles also depend on your theme’s editor-style.css. If it sets specific fonts for paragraphs, you’ll need to override these too.