I think either ur browser has some problem, or rather u shud try to get ur eyes checked >.>
Here's the Post options bar view to different user levels:
A normal member's view to other member posts:
A normal member's view to his own posts:
A Moderator's view to normal member's posts:
A Moderator's view to another Moderator's posts:
A Moderator's view to Admin's posts:
An Admin's view to a normal member's posts:
An Admin's view to a Staff member's post:
Well I've tried my best to find them out just for ur reference, there maybe more views. It all depends upon the permissions set for each user.
So u see normal members have the option to delete their own post [X], so if ur looking forward to deleting sumone else's, that isnt permitted. But make sure u clear ur cache/temporary internet files, thats one of the reasons that can lead to wrong loading of a webpage. If u still do not get the view as shown above (the [X] button to delete), reply back.