Does the web  part utilize content that may not be published? Or that has
item-level security?

Thanks for the reply. I don't think so. For example  the one that I
quoted is just a list of links  to other web  sites which are all public.

What troubleshooting steps have you taken so far? Have you checked  to see if
the permissions  inheritance is broken on the links  list? Can the users see the
links list AllItems view? Is it just web  parts that display  list items that are
causing problems?

Thanks for the reply. In my earlier e-mail I named an example  webpart
but I should have said that SharePoint calls it a "Summary Link Web
Part". I'm not sure about the answers to any of your questions other
than the first. As a normal user I can't see the allitems view of that
webpart at all. In fact there doesn't appear to be any way for a normal
user to get any view other than the error  message I mentioned earlier.
As an administrator  I cannot find anywhere that shows me a "links list"
related to this web  part so I have no idea  whether the permissions
inheritance is broken or not. I assume there is a list somewhere that
the summary Link Web part  uses to store its data but I have no idea
where that is.

It seems to be either "Summary Link" and "Content Query" web parts  that
are broken.

This is a shot in the dark, but maybe check the web  part "Target Audience". If
the audience isn't compiled, or is no longer available, maybe it throws this
error?

You'll need appropriate permissions  to do this:
On the page, click on the little arrow on the upper-right of the web part  and
select "Modify Shared Web Part". On the tool pane that opens on the right side
of the screen open  up the Advanced settings section. You should see Target
Audience. If it's showing a GUID, you may have a problem. If it is empty or
displays an audience name, all should be well.

Thanks for the reply and sorry to take so long to reply - I've been off
work for a couple of days. Anyway, I checked  that but sadly the field
was blank. I think I will try a reinstall  but I did wonder if there was
a possible quick and dirty fix. I have been doing backups religiously
and can go back to a time when it was all working. However, doing this
will result in some losses as updates carried out since that time (about
4 weeks ago) will be lost obviously. However, if I were to restore on
top of the existing sites rather than delete and recreate them will the
restore delete information that isn't in the old backups? I guess it
will but perhaps there is an option (or a hope) that it won't.

What I would really like to do is create a new site  alongside this one,
restore everything and then see what the differences are so that I can
work out what is wrong with this one. I'll maybe give that a god
tomorrow.

The summary Link web  Part and the Content Query Web part  are often used
to summarize content from other sites within the site  collection. I
suspect that permissions  have changed on one of the child sites that is
referenced by these webparts.