There are two issues to be aware of when using EW V4 on Windows 8.
The Windows 8 Upgrade Advisor
If you run the upgrade advisor it flags EW V4 as one of the items for you
to review and says there's an update available.

The link it gives takes you to the normal Microsoft Expression Web page
with no mention of any upgrade.
Bottom line? You can ignore this warning. EW will work as normal
Installing a fresh copy of EW V4 on Windows 8
If you install EW V4 on Windows 8 you'll probably do so from the basic
version, ie with no service packs installed. (Although some download
versions may include the service packs).
When Windows 8 next runs Windows Update, or maybe you run it manually, it
doesn't find SP2 as being available for EW.
The solution for this is to download and run the version created to fix
licencing issues, mentioned on the Expression Forum and in this
Knowledgebase article.
http://support.microsoft.com/default.aspx?kbid=2635101
This includes SP2 so once you've installed this you have the latest
version of V4.
Note that there is another fix mentioned in a general article about
licensing and activation issues, although I can't verify that this works. See:
http://support.microsoft.com/kb/960480/en-gb
NOTE: The free download version will also fix the
licensing issues BUT will negate any support options you may have with your
purchased version of Expression Web.