Using any third party Web Parts? This was a common problem in WSS v2. If
I recall, I think that moving the DLL to the GAC or increasing the trust
level for the assemblies running on the page  from the bin would solve it
(I know that the message doesn't say that). FrontPage demanded Full
trust, not sure about SPD.

I have the same issue.

I made a copy of the troubling page  and deleted ALL webparts in it.
I still can't open  it with the SP Designer – got the same error.

Any clues?

It must be a component that is not in a Web Part zone. What other
components are on the page?

A few things...

You can go into the site  via Start/Run/ then typing \\servername\sites
(or other name you set)\sitename like Windows Explorer and replace
the default.aspx page  with one from a "good" site. That will work
but replace any customizations or text in a content editor web  part.

If this is a web part  page (not the default.aspx) you probably don't
want to use this approach. We ran into a similar issue when we went
from wss 2.0 to SharePoint 2007. We had to retrieve the old files
from the 2.0 version, save them to our hard drive, then upload them
again into the 2007 version site and then we had to reapply the
master page template in SPD and also reset. The problem seemed to be
that it didn't know what template to connect to in 2007. The end
user also somehow modified the code behind the page incorrectly and
the navigation was in the wrong place (probably part of the problem
too).

I've just found the answer an hour ago in ExpertsXExchange:

"Navigate to the site  causing the problem and add the following to
the URL

?contents=1

For example:

http://sharepointsites/default.aspx?contents=1

If you see any web  parts that show an error, try removing them and
then try sharepoint  Designer again."

It works perfectly!

With this you will access the "WebParts Maintenance Page".
Shouldn't it be an easy/documented access for it?

Depending on your version of SharePoint, that page  may show up as a link
on the error  message page.

This is normally the page  you will be prompted to go to when a web  part
won't display in the browser properly. Since the page displays in the
browser, but won't load into SharePoint Designer I doubt the web parts
maintenance page will show any web parts  with errors.

The thing is that the WebParts in error  do not show up in the page.

I even made the test with a page  with no WebParts: I deleted all web
parts, one by one, from one of the pages that had the error in
SPDesigner, and I end up with a blank page but still with the error.
Then I went to the WebPart Management Page, and there it was the
WebPart in Error!

If you deleted all the web  parts from the page  and still had a webpart
show on the web part  management page then you must have closed a web
part at some point in time. Closed web parts  are officially still on
the page they just don't show up. To delete them you need to go to the
closed web parts gallery, re-add them to the page, and then delete them
instead of closing them.

I've been to the "closed webparts" in one of the pages and there they
are! The webparts in error!

You can also append ?contents=1 just after the default.aspx page  and
manage all open  and closed web  Parts from the Web Parts Maintenance
Page. Web Parts should only be closed if your intent is to retain their
personalization.

I'm not using any third party web  parts; only the standard Sharepoint
web parts.

Closed Web Parts (as per a separate thread)?

I'm not sure what you're asking me...

If you browse to default.aspx?contents=1 are there any Web Parts on the
Maintenance page  that could be causing the unsafe error  message? SPD
could kick this error for Web Parts that are closed on the page.

When I browsed to this my page  did not change...there were no errors
shown. If I don't have any errors, should the page look differently?
I'm not sure what I'm supposed to see differently when I add the ?
contents=1 on the end.

You should see the web  Part Management page  instead of the page itself,
which will list all web parts  on the page, open, closed, erroring, and
otherwise. If the page in question already has a query string (e.g.
?name=value) in it, you need to add "&contents=1" (no quotes) instead of
"?contents=1" to the end.

From there you can tell definitively if the page  in question has Web
Parts or not. Try deleting all Web Parts and then attempt to open  the
page in SPD. If you still get the Web Part Unsafe error, then try
opening the site  (not the page) with SPD and look to see if there is a
blue dot to the left of the default.aspx page. If so, right click on it
and select Revert to Site Definition. Then report back.