Ability to enter a caption directly when editing an image

Handling this inside Wysiwyg itself won't happen. We need to focus on integrating the editors and leave the rest up to plugins. Changing this to a support request instead.

If this is possible depends on which plugin you are using to insert the images.
CKEditor's own image dialog for linking to images does not have this feature, though several Drupal modules for uploading/inserting/linking to images do.
For example, both Wysiwyg imageupload (TinyMCE, CKEditor, FCKeditor) and Image Assist (TinyMCE only) provide fields in their editor plugin dialogs for adding captions/descriptions to images that will display below them when the content is rendered.

Due to Wysiwyg module not yet being able to abstract the various editors' selection handling these plugins can not easily render the caption inside the editor as well. Normally, they add at least one wrapping div around the rendered image to keep the caption together with the actual img tag, which works great in rendered contents. However, while editing the contents, Wysiwyg does not know the wrapping div belongs to the plugin which inserted the image, so it won't replace it when the plugin needs to update the contents. Because of this, the image handling modules are limited to using just the images themselves as placeholders during editing, and force caption editing to be done via their dialogs.

For the next major version of Wysiwyg we'll rework this part of the plugin API so they'll hopefully have better control over the contents they insert.

Hope that answers your question.