How can I batch rename files using the Terminal?

First, do a dry run (will not actually rename any files) with the following:

for file in *.mov
do
  echo mv "$file" "${file/MP4./}"
done

If it all looks fine, remove the echo from the third line to actually rename the files.

I just successfully used Automator (first time I've bothered), and it works really well. I saved the automation as a Service. It took about 10 seconds to make something easily reusable:

1. Open Automator.
2. As type of document, choose "Service".
3. Change Service receives selected "Text" to "files and folders".
4. Consider changing "any application" to just Finder.
5. From the sidebar, select "Files & Folders" (under Library) and from the listed actions, in the center column, drag "Rename Finder items" to the right side and drop it within "Drag actions or files here to build your workflow."
6. Change the action you just added from "Add Date or Time" to "Make Sequential".
7. Click "Options" at the bottom of the action and check the option "Show this action when the workflow runs".
8. Hit "CMD+S" to save the service as something like "Replace Text"..
9. Done!

Now you can right-click any selection in Finder, go to the Service menu and select "Replace Text", fill in how you want the text changed or replaced - and click "Continue" to apply configured changes.