Is there a facility in EPiServer to search and repace content for the entire site? i.e. ) if I have a dead link that I know exists on some of the pages, how would I search and replace this link?
Not for external links I'm afraid. I would create a schedule jobs that checks for broken links and creates a report in the report center. Simply displaying all pages and which properties contains the broken links. You could also create some functionality that automatically replaces the links with a new link. For internal links I believe there is such a scheduled job already.
This is a commonly requested feature that unfortunately isn't included in EPiServer. There has been some SQL scripts floating around that would do exactly this, but that wouldn't be a method I would recommend for a production environment as it would update the current published version without creating a new.
It should be fairly easy to create a plug-in, that can do this using the API. FindPagesWithCriteria to find the page and just standard string manipulation to replace the text and finally update the page the using the standard Save method of the DataFactory. Just a warning for the possibility of this being quite slow for larger sites.
Hope that helps!