Hi Filip,
remember to move any cron jobs.
Moodle usually has an administrative script that runs every few minutes and does things like recalculate completions, and other tasks for core and plugins.
http://docs.moodle.org/23/en/Cron
A rare case is an SMTP configured to an IP of the local network to the old host, but I hope that is not your case You can search SMTP in the admin search box to see if there's anything.
The maintenance mode and the CLI maintenance mode are also useful when switching, to avoid DB modifications during the switch.
http://docs.moodle.org/22/en/Maintenance_mode
Good luck.
EDIT: Make sure you have all the php extensions needed. On Ubuntu suggested way to install them is:
sudo apt-get install php5-curl php5-gd php5-intl php5-xmlrpc
plus apache restart
http://docs.moodle.org/23/en/Step-by-step_Installation_Guide_for_Ubuntu
Maybe the Migration Wiki could be more clear about these steps, even though cron manual is linked in the sidebar.