We recently had to move three websites out of a WP Network ("multisite") installation. We took notes while we were working on this, but as it turned out almost everything we had to do was already documented in this excellent tutorial.
The one issue we did run into was a problem where our admin user was not allowed to access the control panel on two of the tree migrated websites. We would login, but then get a "Not Allowed to Access this Page" error when trying to access /admin. We eventually traced this to a permissions issue, where our previous network admin user did not have admin permissions on the two problem websites after completing the migration.
The solution was to go into the wp_n_usermeta tables on the two problem websites and change a table prefix in the meta_key column for our user. The two websites were using the table prefixes wp_3_ and wp_4_, corresponding to the old multisite id numbers, but our user with user_id = 1 only had an entry with the meta_key wp_capabilities and the meta_value administrator. Changing that meta key to wp_3_capabilities and wp_4_capabilities solved the permissions problem.