New WordPress Post is not showing up or displaying for some people: I get this question quite frequently and in almost every case, the Post is flagged as Private. The reason most bloggers think it has been posted and is viewable to the public is because private posts are viewable to those that are logged in with administration access rights and typically after a blogger writes and publishes a post, they go View site without logging out. So, the post shows up for them as the browse the site.
Making sure the post is Published not Private:
Login to your WordPress Admin Panel.
Select Manage -> Posts from the Menu, navigate to the post in question and click Edit.
Under Post Status, ensure that the Published option is checked and then click Save or Publish.