I started using TweetDeck recently. It seems to work rather well but there were a couple problems after the installation on my 64bit Ubuntu system.
I was getting the following error when running from the command line
Error loading the runtime (libadobecertstore.so: cannot open shared object file: No such file or directory)
To fix this error you should just need copy the libadobecrtstore.so to the lib32 directory
$ sudo cp /usr/lib/libadobecertstore.so /usr/lib32
If you still get other problems you may also need to install a couple other libs.
The best way to do this is to use a package called getlibs. This system automatically resolves 32bit lib problems on 64bit systems.
You can download the deb package from http://frozenfox.freehostia.com/cappy/getlibs-all.deb
Then run the following command to download and install all the libs
$ sudo getlibs -l libnss3.so.1d libnssutil3.so.1d libsmime3.so.1d libssl3.so.1d \
libnspr4.so.0d libplc4.so.0d libplds4.so.0d libgnome-keyring.so \
TweetDeck should now be ready to go.