The errors are telling you that the Qt libraries that are available on the PATH do not match the ones Sigil needs.
On Linux, you cannot run the "sigil" executable directly. You need to run "sigil.sh". That sets up the LD_LIBRARY_PATH environment variable and starts Sigil. All of this is done so the Qt libs the installer places in the /opt/sigil dir are picked up during load.
The desktop and the start menu shortcuts call this shell script for you, use those.
This all pertains to Sigil installed from the provided binary installers. If you compiled the source yourself, you can just call "sigil" since you need >Qt 4.6.0 on the PATH just to compile the sources.
This behavior is nothing new and has been present in several previous versions of Sigil.