I'll assume you mean Mail.app and not Safari.app here; the former is mail, the latter is web.
If you're using Mail.app to access your mail, try rebuilding your mailbox (select the inbox mailbox with the weird dates > Mailbox > Rebuild) and see if that clears the issue.
If not, test with a different mail server; see if the problem is specific to one mail server, or if Mail.app is doing something very weird.
If you really meant that you're using Safari.app here and that you're using a web mail client to access your mail, then there's likely a problem with whatever service that you're accessing with the web mail client. Please contact the maintainers of the web mail service for assistance.