This error message is a null reference exception from TOM or the TOM.NET API. Unfortunately, it is also very difficult to quickly track down the error and you'll have to do some hunting around to find out.
If you are using Compound Templates, you can try to preview the Page Template with the page and see if you get a better error message with a line #. You can also try to preview each of the Component Templates with the Component to see if it breaks.
Maybe if you are using WebDAV URLs to open a Components, and the WebDAV URL is hard-coded you would have an object without a value, and then when you try to access a property or method of that object you will have this error.
You would have the same with a URI reference, but I would guess all the URIs in the child are also in the Parent.
Finally, you might want to check if any of the templates are localized, since they could change the URI in the template and it would not find the object.