Here is how to reproduce this bug:
 * Download http://fgouget.free.fr/bugs/testdep.tar.bz2
   This is a small archive that contains a set of test, empty, Debian package files along with their source.
   (run ./build to rebuild them)

 * Install the testdep-allsarch_1.0-1_all.deb package.

 * Then run the following command and install the package:
   qapt-deb-installer testdep-allsarch-default_1.0-1_i386.deb
   (on a 64-bit system, on a 32-bit one replace i386 with amd64)

The command will appear to succeed but in fact it leaves the testdep-allsarch-default broken. The problem is that qapt-deb-installer seems to think that architecture all packages can satisfy the dependencies of packages of any architecture. That's wrong. In fact they can only satisfy the dependencies of other architecture all packages, or of packages in the system's native architecture.

Here the testdep-allsarch-default package we try to install is not in the system's default architecture and thus its dependency on testdep-allsarch cannot be satisfied.

Note that this is also true of multiarch architecture=all packages. For instance one can also reproduce this bug with the following package combination (from the set of test packages):

* Install testdep-allallowed_1.0-1_all.deb (a multiarch=allowed, architecture=all package)
  Run qapt-deb-installer testdep-allallowed-default_1.0-1_i386.deb

Note that this is actually 'part two' of bug 330448. It turns out it's a bit more important that I first realised.
This is also somewhat related to bug 330446 in that it's multiarch=foreign packages that can satisfy dependencies for any architecture instead of architecture=all as qapt-deb-installer seems to think. The fix to the two bugs is probably different though.

* Bug 330446: qapt-deb-installer fails to detect and report some installation errors
  https://bugs.kde.org/show_bug.cgi?id=330446

* Bug 330448: qapt-deb-installer mishandles dependencies on multiarch=foreign packages
  https://bugs.kde.org/show_bug.cgi?id=330448

ProblemType: Bug
DistroRelease: Ubuntu 13.04
Package: qapt-deb-installer 2.0.0-0ubuntu1
ProcVersionSignature: Ubuntu 3.8.0-26.38-generic 3.8.13.2
Uname: Linux 3.8.0-26-generic x86_64
ApportVersion: 2.9.2-0ubuntu8.1
Architecture: amd64
Date: Sat Jul 27 00:23:06 2013
InstallationDate: Installed on 2013-04-29 (88 days ago)
InstallationMedia: Ubuntu 13.04 "Raring Ringtail" - Release amd64 (20130424)
MarkForUpload: True
SourcePackage: qapt
UpgradeStatus: No upgrade log present (probably fresh install)

Reproducible: Always