I have installed 2.4.1 on the web server with the black candy theme before adding custom theme etc. After much trial and error and reloading I am down to three problems (I think!). In no particular order:

1- to access the cms/flush I have to include index.php in the address- for example, ip address/~domain/index.php/admin (test site on Nucleus isp)
2- seem to be in an infinite loop continually being asked to login, or rather, login as someone else.
3- page type says "change to error page" on most pages - (PHP for custom pages has been uploaded)

Rebuilding the database includes the below each time

# Page
# Index Page_versions.RecordID_Version: changed to unique (RecordID, Version) (from unique (RecordID,Version))
# Homepage
# Index Homepage_versions.RecordID_Version: changed to unique (RecordID, Version) (from unique (RecordID,Version))
# Quadpage
# Sidebarpage
# Index Sidebarpage_versions.RecordID_Version: changed to unique (RecordID, Version) (from unique (RecordID,Version))
# SiteMap
# Wines
# Index Wines_versions.RecordID_Version: changed to unique (RecordID, Version) (from unique (RecordID,Version))
# ErrorPage
# Index ErrorPage_versions.RecordID_Version: changed to unique (RecordID, Version) (from unique (RecordID,Version))
# RedirectorPage
# Index RedirectorPage_versions.RecordID_Version: changed to unique (RecordID, Version) (from unique (RecordID,Version))
# VirtualPage
# Index VirtualPage_versions.RecordID_Version: changed to unique (RecordID, Version) (from unique (RecordID,Version))

Any help would be very much appreciated.

=====Note - have just read in a post that duplicating the page and renaming solves the page type problem.=============

index.php still needs to be included in the address

mod_rewrite doesn't sound like it has been correctly setup on your server. You will need mod_rewrite to use 'nice' urls like /page/. Check with your host whether you have access to mod_rewrite and ensure there is a '.htaccess' file in your websites root folder (windows may hide this file from you but it needs to be there)

=still being asked to log in when accessing a draft page. (all pages have been published automatically)

This is standard. You have to login to see draft content.

I have what I believe is a related problem.
I have a site I am developing, and things are going great.
If I load http://testsite.local the site loads perfectly to the home page as I would expect.
If I load http://testsite.local/index.php the html for the page loads but every element linked to the page is looking for something like: http://testsite.local/index.php/index.php/sapphire/thirdparty/behaviour/behaviour.js?m=1267739533 (this is one of the JS includes toward the bottom of the page), and any locally referenced items from my themes directory are failing to link, so I can only guess they are being routed as: http://testsite.local/index.php/index.php/themes/...etc...

now this is all running on my local xampp install and I have other sites I have developed on this install as well, and it seems fine.
Does the .htaccess included with silverstripe know how to reroute the request to index.php? or..

Christy did you have any luck getting past this?

Ahhhhhh don't know!

Allowoverride was set to all and mod_rewrite enabled. (Thanks, Willr)

On the test site - before the A record was pointed to it - I solved the index.php problem by following this post:
http://www.silverstripe.org/general-questions/show/292147#post292147

and adding below to the .htaccess file.
RewriteBase /sssite
RewriteCond %{REQUEST_URI} sssite$
RewriteRule (.*) $1/ [L]

When the site went live, it was including an extra /sssite/ in the address but working OK - if that makes sense.

The lines added to the .htaccess file have been removed and address is as it should be.

But why?? That is the question?