"Migrating undefined" or "[undefined][undefined]"
There may come an instance where the process will get stuck while migrating data for a specific component and (with "Debug mode" enabled) an error similar to "Migrating undefined" or "[undefined][undefined]" will be displayed.
Some causes and remedies include:
1) a migrate_xxx.php file that is being requested for by jUpgrade is not available or accessible
(these files are stored in the {root}/administrator/components/com_jupgrade/includes/ folder, labelled "migrate_xxx.php" where "xxx" is the section of content being transferred at the time.)
To fix: uninstall and reinstall jUpgrade (to restore all required files) and try again.

2) the database table from which content is being transferred is corrupt or has been modified
(jUpgrade requires that no modifications have been made to any of the core tables themselves, otherwise the migration can run into problems when dealing with custom fields)
To fix:download and install a maintenance component such as "Admin Tools!" and run a database integrity check and repair. Alternatively the database may have to be repaired manually using "phpmyadmin" or a similar interface. A solution for databases with custom fields is being looked into, but for the moment those must be migrated manually, or if they interfere with the migration, removed. (Of course a backup should be run before any such operation.)

3) the migration runs into an issue attempting to copy content over to a database which already has content (from a previous migration, failed or not).
To fix: remove all the tables created for the new Joomla! install during the migration and run jUpgrade again.

4) the Javascript which handles the migration process has run into a problem
To fix:check in the Plugin Manager to ensure that any system plugins related to javascript libraries, apart from the "MooTools Upgrade" plugin (which is required) has been disabled and try running jUpgrade again.