Members of a new or existing role do not have the options that are desired in the Right click menu.
For example they have Delete rights in the Role they are a member of but they cannot Right click to delete a computer.
Some common Item Tasks are:
Remotely Control With Carbon Copy
Security Role Management
The Security Role that the user is a member of does not have all of the appropriate permissions.
The Right click menu security is controlled by the Item Tasks, the role needs to be given read rights to the item that you are trying to allow them to see.
NS 6 Pre SP2
Configuration Tab> Configuration> Server Settings> Notification Server Settings> Item Tasks> (desired Item Task) Add Role and assign it the Read System permission.
NS 6 SP3
1. Configuration Tab> Configuration> Server Settings> Notification Server Settings> Security Roles
2. Select the desired Role
3. Click the 'Show Security Role Manager Console' button
4. Set the 'Filter' in the upper right hand corner to 'All Items'
5. In the tree browse to Server Settings> Notification Server Settings> Item Tasks
6. Select the desired Item Task and give them Read rights.