A Web Part or Web Form Control on this Page cannot be displayed or imported. You don't have Add and Customize Pages permissions required to perform this action
This error occurs in Sharepoint 2010 or when you upgrade to Sharepoint 2010 from MOSS 2007.
It clearly says, adding a webpart/webcontrol to this page is not possible, since the user who adds doesnt have Add / Customise Page permission.
Solution :
(a)
Fix for that User alone
Add the below permission to the user / group.
(b)
Fix for the webpart(s) for any user
Check which webpart created this error. The commonly/mostly used Content Editor Webpart is the culprit for us. So added the below entry in the web.config. If its other webpart, add Assembly, Namespace and TypeName accordingly.

Before going for the fix, lets see why this was working in MOSS 2007 and not in Sharepoint 2010. or what is broken when you upgrade to Sharepoint 2010 ??
Well, nothing is broken. Its just Sharepoint 2010 which was
coded to have more granular security.
In the previous version(s) - MOSS 2007 (im not sure about 2003, but it also works the same i hope). My team mate was so eager to know the reason before fixing.
So, I checked the web.config of a MOSS 2007 web application and it had the above kind of entry, but for all webparts !!

ie., Type/TypeName = "*" (any class in that assembly is registered as safe & AllowRemoteDesginer was true. )
Also, I tried using reflector and checked the two DLLS (MOSS 2007 - Microsoft.Sharepoint.dll & Sharepoint 2010 - Microsoft.Sharepoint.dll )
Where I found few methods like below defined in 2007 DLL is not present in 2010 DLL.

Simply to put up, for granular control instead of having TypeName= "*" - we have each and every webpart defined in the safecontrol !