I do not use the Ubuntu Software Center to install LO or the Desktop Integration files. I use the terminal.
I remember the Ubuntu/Unity top bar menus work for me before. But I reinstalled 12.04 on that machine after I tested 13.04. I have not updated LO on that laptop, yet, to 4.0.3. Though I do remember using LO 4.0.3 with Unity once. I prefer MATE desktop environment over Unity on my desktop, but I decided to leave at least one laptop with only Unity installed as a d.e.. The other laptop is being used as a testing platform for Linux Mint and other Debian based distros.
4.0.4 comes out before the end of the month. If this was an issue or bug known before, then it is a good bet that the 4.0.4 version might have fixed it.
But to satisfy something that is in the back of my mind about a previous issue I had with Ubuntu Software Center and LO, could you try re-installing the desktop integration folder within Terminal?
Just open up the terminal and "cd" into the "desktop-integration" folder
it will be something like this
cd LibreOffice_4.0.3.3_Linux_x86-64_deb/DEBS/desktop-integration
or
cd LibreOffice_4.0.3.3_Linux_x86-64_deb
cd DEBS
cd desktop-integration
Then do
sudo dpkg -i *.deb
That is how I deal with my installs for LO, and through the Ubuntu Software Manager.
ALSO
How did you get rid of the Ubuntu 12.04 version's install of LO?
There may have been some file or package from the older version that should have been removed before you install the 4.0.3 version. I found that to be very true when I was testing Ubuntu 13.04. I do know that if I do not remove all parts of LO's link to the desktop environment's menu system from the previous install, there can be some issues crop up with the install of the new version's access to the menu system for the desktop.
I do not know if this will help you, but is did me with 12.04, 12.10, and 13.04, from time to time, whether running Unity or MATE for a desktop.