Unable to display this Web Part. To troubleshoot the problem, open this Web page in a Windows SharePoint Services-compatible HTML editor such as Microsoft Office SharePoint Designer. If the problem persists, contact your Web server administrator.

This problem occurs if the site is saved as the template and restored onto another server.
The resolution is given here, I wont repeat to avoid unnecessary redundancy

But in brief, therotically solution is

we have to add curly braces to the list ID

We have to do this before saving the site as site template. There are some five occurences of the site ID which we need to change, we just have to add curly braces to the listID then only designer generates the new list IDs for these webparts.