The problem is that when you open (or edit an existing) issue, there is no edit button as well as the mentioning feature is not working.
This unexpected behavior is appearing because you of the following thing - please go to Administration (on top) - Settings - General. And here, on Text formatting it is set to be none value. Indeed this is the root of the problem. Please change it to either Markdown or Textile and apply the changes.
Afterward, both features Zenedit button and mentioning will start working.