Currently there is no way to search for a specific message in the inbox. 

I have dozens of messages, spread over a large number of pages. The only way to find a specific message is to go page-by-page. A search box on the description field (similar to other pages like for Opportunities) would be very helpful.

Hi Ali. No, no particular message. But I can have many, many pages of messages in  the inbox. It seems like the inbox function has not been given a  lot of love - you can't organize them, you can't show all at once to use a browser text search, and you can't search the content. You can't find all unread messages, and you can't mark them as read without actually opening each one. But I'd say the content search option is the most needed. 

Beth