I'm using Rational ClearCase and I'm a little uncertain how to proceed and can't find much help online.

I'm attempting to deliver several tasks, some of which involved moving around some folders in child directories (in case that's relevant).

When I go to Deliver From Stream to Default, I get the following error:

An error occurred during the Deliver operation.
An error occurred while checking out or merging the directories in the target view.

Clicking OK reveals a little more information, but nothing I've been able to use:

Unable to checkout the directory element "xxx". This may cause additional checkout and merge failures for files and directories contained within
An error occurred while checking out or merging the directories in the target view.
Unable to perform merge.
Unable to do integration.

When merging, the parent directory has the Status Unknown Error while all other child directories have a status of OK:

screenshot

I've tried the suggestions on Deliver fails with an error while checking out or merging the directories in the integration view:

The integration stream is definitely not locked.

When I try to search for checkouts with the command line:

cd <integration_directory>
cleartool lsco -r

I get the following error:

cleartool: Error: Not an object in a vob: ".".

I've delivered to this project dozens of times without getting any such errors.

Q: Where can I go or what can I do to begin troubleshooting this?

Any kind of error on a snapshot view during a merge (or an UCM merge: a deliver) means an update issue.

Usually, a merge (or deliver) using as a destination view a snapshot view starts by updating the view.
But if that view was partially updated, the merge won't be able to proceed fully.

Hence the need to do the update, always from the root of the view (and not one of its sub-folders).