I've looked at the sources, and the problem seems to be sqlite not supporting 
unicode
lower/upper transformations. It requires an ICU extension that seems to be 
missing in
the version that Android ships.

I've hacked a patch that leaves the UPPER() to sqlite for the pattern too. This 
at
least makes exact matches work, since sqlite doesn't touch the accented 
characters.

I also did a little change that seems to fix this error trace:

E/AndroidRuntime( 9671): Uncaught handler: thread Searcher #3 exiting due to 
uncaught
exception
E/AndroidRuntime( 9671): java.lang.IllegalArgumentException: the bind value at 
index
1 is null
E/AndroidRuntime( 9671):    at
android.database.sqlite.SQLiteProgram.bindString(SQLiteProgram.java:174)
E/AndroidRuntime( 9671):    at
android.database.sqlite.SQLiteQuery.bindString(SQLiteQuery.java:190)
E/AndroidRuntime( 9671):    at
android.database.sqlite.SQLiteDirectCursorDriver.query(SQLiteDirectCursorDriver.
java:55)
E/AndroidRuntime( 9671):    at
android.database.sqlite.SQLiteDatabase.rawQueryWithFactory(SQLiteDatabase.java:1
118)
E/AndroidRuntime( 9671):    at
android.database.sqlite.SQLiteDatabase.queryWithFactory(SQLiteDatabase.java:1006
)
E/AndroidRuntime( 9671):    at
android.database.sqlite.SQLiteDatabase.query(SQLiteDatabase.java:964)
E/AndroidRuntime( 9671):    at
android.database.sqlite.SQLiteDatabase.query(SQLiteDatabase.java:1078)
E/AndroidRuntime( 9671):    at
vu.de.urpool.quickdroid.apps.AppProvider.query(AppProvider.java:111)
E/AndroidRuntime( 9671):    at
android.content.ContentProvider$Transport.query(ContentProvider.java:129)
E/AndroidRuntime( 9671):    at
android.content.ContentResolver.query(ContentResolver.java:149)
E/AndroidRuntime( 9671):    at
vu.de.urpool.quickdroid.apps.AppLauncher.getSuggestions(AppLauncher.java:67)
E/AndroidRuntime( 9671):    at
vu.de.urpool.quickdroid.Searcher$AsyncSearcher.run(Searcher.java:81)
E/AndroidRuntime( 9671):    at
java.util.concurrent.ThreadPoolExecutor$Worker.runTask(ThreadPoolExecutor.java:6
48)
E/AndroidRuntime( 9671):    at
java.util.concurrent.ThreadPoolExecutor$Worker.run(ThreadPoolExecutor.java:673)
E/AndroidRuntime( 9671):    at java.lang.Thread.run(Thread.java:1058)

I'd love to see it search in accent-independent way:
Many keyboards don't support accents well, so if I was able to type "Slawek" 
and it found "Sławek" too.

It would be a great improvement for me, especially as the default contacts 
search doesn't support it (a pretty significant hit, as my 5-year old WinMo 
phone had proper contacts lookup).

Now I'm using Android 2.3 and it finds accented names if I type them 
explicitly, but it's suboptimal.