What Permission is needed to attach a file to a Comment?

The error would indicate the users are uploading a file with an extension that is not allowed on the site.

Administrators by default will have "Bypass Validation" permissions, that is why they do not receive this message.  Regular users by default are limited to allowed file extensions and file sizes.  The file extensions allowed are defined in the administration panel.

Globally under Moderation files and for each application in the Applications section of administration.  The application lists can not add new extensions, they can only limit the global list further for that application (i.e. if pdf is not allowed in the global list, they will not be allowed if added to the Blog application).

The error would indicate the users are uploading a file with an extension that is not allowed on the site.

Administrators by default will have "Bypass Validation" permissions, that is why they do not receive this message.  Regular users by default are limited to allowed file extensions and file sizes.  The file extensions allowed are defined in the administration panel.

Globally under Moderation files and for each application in the Applications section of administration.  The application lists can not add new extensions, they can only limit the global list further for that application (i.e. if pdf is not allowed in the global list, they will not be allowed if added to the Blog application).

The user is trying to upload PDF or PPTX.  Both are allowed

This error is only used after a file extension check fails, can you post a screenshot of you global and application (where this is failing) settings for file extensions.  Perhaps there is an issue with the list of allowed extensions.

I can duplicate this with Blogs and File Galleries, but not Forums.  Granting bypass validation permission does not resolve the issue neither does changing the member to a manager.  Wikis don't have bypass validation permission

I haven't been able to reproduce this yet.  Can you give me the steps you are following to cause the issue?

In a Comment Editor, I Select Insert --> Insert Image/video/File --> Change From to File Upload  -> Browse for a file - Then Click "OK".   Same steps that I used to upload the image files above.

From inside the activity stream or from inside each application?  Do you see the same error in both locations?

Inside each application.  Same error.  Also, I can duplicate the same error in user file add

Apologies if this has already been investigated, but have you also verified that the file types are allowed in the specific applications, themselves, and not just the overall application type? In 10.1, there's basically 3 stages of verification:

1. Site-wide global allowed file extensions in Administration > Moderation > Files
2. Allowed file extensions for the application type in Administration > Application > [Application Type]
3. Allowed file extensions for the application by visiting the application and navigating to the Pencil Icon > Manage > File Options.