Issue

When there are multiple web applications in a SharePoint farm, and the "My Workflow Tasks" web part is added to a site or site collection page and configured to retrieve assigned workflow tasks at the farm level, the result below might occur: 
Only the workflow name is returned for workflows that are running on the other web applications. Other fields such as item, status, waiting since, approver and current action are left blank.

Resolution

Ensure the application pool accounts of each web application has access to the SharePoint content databases of the other web applications in the farm. 
"AppPoolAcc1" of "WebApplication1" should be configured to have access to SharePoint content database of "WebApplication2" and vice versa. 

Below PowerShell command can be used to grant access accordingly. 

$webApp = Get-SPWebApplication <<webApplication2 URL>> 
$webApp.GrantAccessToProcessIdentity("domainusername of WebApplication1 app pool account")