Hi I'm a new monero user here ( I was waiting for the gui) , I've managed to run successfully Monero GUI on Ubuntu 16.04.1 and Lubuntu 16.04.1 from a full installation on an usb stick on a very old laptop (and using an external daemon), hence why I switched to lubuntu which runs much better.
I encountered the problem you describe I did the following to solve it:
sudo apt-get install qml-module-qt-labs-settings qml-module-qt-labs-folderlistmodel
sudo apt-get install qml-module-qtquick-controls
sudo apt-get install qml-module-qtgraphicaleffects
If you want to speed up even more I tried the following on lubuntu after ditching ubuntu
sudo apt-get install libunbound2
and then do:
set QMLSCENE_DEVICE=softwarecontext ./monero-core
set QMLSCENE_DEVICE=softwarecontext ./monero-wallet-gui
and then start
If the above command will not start the GUI try
Be aware that I think there is a bug when you create a wallet from a seed it just sometimes does not led pass to the next screen, the right arrow control is not activated but if you start typing on the name of the wallet, the right arrow control activates and then you can click to the next screen with the wallet recreated.
Hope it helps.