Comment 3 for bug 1194743

The following is indicative of a corrupt package:

Jun 26 06:53:42 ubuntu ubiquity: Preparing to replace libreoffice-core 1:3.5.4-0ubuntu1.1 (using .../libreoffice-core_1%3a3.5.7-0ubuntu4_i386.deb) ...
Jun 26 06:53:42 ubuntu ubiquity: rmdir: failed to remove `/var/lib/libreoffice/basis3.4/program/'
Jun 26 06:53:42 ubuntu ubiquity: : No such file or directory
Jun 26 06:53:42 ubuntu ubiquity: rmdir: failed to remove `/var/lib/libreoffice/basis3.4'
Jun 26 06:53:42 ubuntu ubiquity: : No such file or directory
Jun 26 06:53:42 ubuntu ubiquity: Unpacking replacement libreoffice-core ...
Jun 26 06:53:45 ubuntu ubiquity: dpkg-deb (subprocess): data: internal bzip2 read error: 'DATA_ERROR'
Jun 26 06:53:45 ubuntu ubiquity: dpkg-deb: error: subprocess <decompress> returned error exit status 2
Jun 26 06:53:45 ubuntu ubiquity: dpkg: error processing /target/var/cache/apt/archives/libreoffice-core_1%3a3.5.7-0ubuntu4_i386.deb (--unpack):
Jun 26 06:53:45 ubuntu ubiquity: short read on buffer copy for backend dpkg-deb during `./usr/lib/libreoffice/program/libooxlo.so'

This means that the package either became corrupted in memory or on disk. I don't see any hardware errors in your log file. I'd try installing Ubuntu without downloading updates. (This is a choice in the beginning of the installer.)