Can't view Exported Batches (DataTables warning)
Okay, solved. There was something awry with the latest Batch in that it had been exported, but the file didn't exist in the custom directory/filesystem. I changed that last batch status directly in the database from 5 (exported) to 2 (closed) and now the screens all load as usual.

I suppose line 335 of /path-to-site/sites/all/modules/civicrm/CRM/Batch/BAO/Batch.php is trying to load information about this non-existent file and causes the error somehow, but I don't fully understand how.

EDIT: The error recurred when we tried to re-export the problem batch, but I was able to get a more helpful error message this time:


  Error: [] operator not supported for strings in CRM_Financial_BAO_ExportFormat_CSV->formatHeaders() (line 166 of /path-to-site/sites/all/modules/civicrm/CRM/Financial/BAO/ExportFormat/CSV.php).


So this is in fact a PHP 7.1 bug. Issue in lab is here. PR is here.