This is an elusive bug... I thought that this would only occur when upgrading a package containing a library and the library was in use by some process at the upgrade time.
Do you have any of forked-daapd, minidlna, mediatomb, or mpd on your system? tried using any of them? and all succeed?
The following packages depends on sqlite: aria2 forked-daapd fuppes lighttpd mediatomb minidlna mpd pyload python sabnzbd svn.
Notice that not all of them necessarily *require* the sqlite libraries. Only aria2, forked-daapd, minidlna, mediatomb, mpd, sqlite and svn are linked with libsqlite3.so, others might just call sqlite3 if needed.