The provided binary is statically linked to specific versions of dependent system & other software libraries.  I was able to get it running by creating symbolic links for the libraries it was looking-for:

(in the respective files/directories)
# ln -s ./libminiupnpc.so.8 ./libminiupnpc.so.9
# ln -s ./libboost_system.so.1.46.1 ./libboost_system.so.1.49.0
# ln -s ./libboost_filesystem.so.1.46.1 ./libboost_filesystem.so.1.49.0
# ln -s ./libboost_program_options.so.1.46.1 ./libboost_program_options.so.1.49.0
# ln -s ./libboost_thread.so.1.46.1 ./libboost_thread.so.1.49.0

However, it is not generally recommended to do this, as if the program is dependent on certain features - you risk your wallet crashing and doing other potentially awful stuff.

Consequently, I resolved to get a Linux wallet to compile from the git-source, as available from the wallet page from the main ultracoin site.

http://ultracoin.net/wallet.html

On Ubuntu 12.04, I specifically needed-to:

- run "qmake" from the install directory ./ultracoin-master
- create a symbolic-link to the ./src/qt/res as ./res
- copy ./src/qt/res/icons/splash2.jpg to ./src/qt/res/images/splash2.jpg
- per the readme, install a lot of libraries on Ubuntu
   > by installing the latest libboost1.4.8-all-dev, it ended-up removing all previous versions of the libboost libraries.
   > on Ubuntu "libdb4.8++-dev" is just "libdb4.8-dev"
- I turned-on all the options I could see, when I ran "qmake"
   > # qmake "USE_UPNP=1" "USE_DBUS=1" "USE_QRCODE=1"

... and after all that, it runs just like the binary I initially "jury-rigged" to get running in the first place.  I mean, the compiled product perfectly emulates what they give, from showing an icon in the Unity display bar, in the upper-RHS, right down-to not listening on TCP/44101 for solo-mining, either! 

OTOH, the days of solo-mining might just about be over anyways...