Can't find edit button

Does the user actually have permission to edit content of that type? (For example, do they have the "edit own content" or "edit any content" permissions for that content type provided by the Node module?) If the edit tab doesn't appear, it sounds like they don't.

They need that permission to be able to get to the edit screen in the first place... the Field Permissions module only controls access to specific fields on top of that.

I'm having a similar problem. Although have more information.
The user has permission to edit their content and can on the node I set to them having authored. If I turn the ability to edit a field off that change works in the node they are set.
If I have Editable Fields module on it screams
"•Notice: Undefined index: module in editablefields_fallback_formatter() (line 173 of /home/medium8/public_html/sites/all/modules/editablefields/editablefields.module).
•Notice: Undefined index: module in _field_info_prepare_instance_display() (line 354 of /home/medium8/public_html/modules/field/field.info.inc)."
at me.
I've tried to uninstall Editable Fields but it doesn't seem to go away. So could be related.

Update. I installed the module on my test system and it had the same problem and the system has never had Editable Fields. I basically removed every module on it and still never worked.
I could just work around this and manually turn fields uneditable except you can't do that with the title field.

Another Update: So I ruined my drupal on my test machine so I installed fresh 7.15 and installed only Editable Fields and it still functioned the same. So I went on the IRC channel and someone said to go to reports and Node Access Permissions and rebuild the permissions. I tried that and it didn't seem like it was doing something. Then I noticed it says Node Access Permissions : Disabled. And I was like that doesn't seem right. So I installed the Access Control Module to see if it changed that and it did. So I went and read other issue reports and found this one. http://drupal.org/node/1728550
It indicates the same thing except for them it is working well enough because the module works in so far as determining what specifically you can do with a field if you can get it on the screen but it does not change the actual ability to open the edit screen if you don't have overall permission to open it.

In order to affect a user's ability to edit content, this module would have to be implementing some form of hook_node_access OR hook_menu_alter. It's not, so I'm pretty sure this isn't our problem.