This is a common problem for people using the plugin, “Advanced Access Manager.” If you do not have this plugin, your problem is something else.
If you use Advanced Access Manager and have noticed that since installing, the checkbox next to each comment is missing, there is an easy fix for you. It took me a while to track down what to do but I was finally able to do it. Here is how to bring to the checkboxes back so you can approve, deny, edit, or spam comments again. Essentially you need to add the function to allow editing comments.
1. Go to your your blog dashboard. On the left, near the bottom of the menu choices, click “AWM Group” and then when the sub-menu opens up under that, click “Access Manager.”
2. In the new horizontal menu that opens up, click the 3rd choice, “Capabilities.”
3. In the bottom-left of this area, select, “Add New Cap.” In the dialogue that appears, name the new capability “Edit Comment.”
That’s it! If you wish to give this ability to more roles (Subscriber, Editor, etc.) simply select that role in the bottom of the window and then check the “Edit Comment” checkbox that we just created.
It baffles me why this capability is not available by default, I’m not sure why you would EVER not want anyone to be able to manage the comments. I am currently running WordPress 3.3.2 and Advanced Access Manager 1.6.2. From my research, it would appear that this problem has existed for a while, though it’s possible it could be fixed in future versions of the plugin.