I tryed to install qt-dev with apt but installation was broken and now I cannot install\remove anything. When I start Synaptic it tells me that I have 33 broken packages. OK, I click Fix Broken Packages and Apply. The package casuing the problem is xlibmesa-gl. Synaptic cannot install it because it will replace (I guess) /usr/X11R6/lib/libGL.so.1.2 and that file is in use by some other package (fglrx), my graphic card driver. I tryed to do apt-get remove fglrx but it can't remove it because of these broken packages. Each and everyone of these "Broken" packages works normally without any problems.. Can someone please tell me how to fix this problem?

Generally you can use apt-get -f dist-upgrade or aptitude -f dist-upgrade to fix a lot of broken packages. The -f stands for "fix broken". Try both apt-get and aptitude because sometimes if one doesn't work, the other will for some reason.

shiva:/home/astral# aptitude -f dist-upgrade
Reading Package Lists... Done
Building Dependency Tree
Reading extended state information
Initializing package states... Done
Reading task descriptions... Done
The following packages are unused and will be REMOVED:
xfonts-100dpi xfonts-75dpi xfonts-base xfonts-scalable xserver-common
xserver-xfree86
The following NEW packages will be automatically installed:
xlibmesa-gl
The following NEW packages will be installed:
xchat xlibmesa-gl xlibosmesa-dev xlibosmesa4
The following packages will be upgraded:
d4x
1 packages upgraded, 4 newly installed, 6 to remove and 0 not upgraded.
Need to get 0B/3194kB of archives. After unpacking 30.9MB will be freed.
Do you want to continue? [Y/n/?]
Writing extended state information... Done
Media Change: Please insert the disc labeled 'Debian GNU/Linux 3.1 r0a _Sarge_ - Official i386 Binary-1 (20050607)' in the drive '/cdrom/' and press enter

(Reading database ... 146158 files and directories currently installed.)
Unpacking xlibmesa-gl (from .../xlibmesa-gl_4.3.0.dfsg.1-14_i386.deb) ...
dpkg: error processing /cdrom//pool/main/x/xfree86/xlibmesa-gl_4.3.0.dfsg.1-14_i386.deb (--unpack):
trying to overwrite `/usr/X11R6/lib/libGL.so.1.2', which is also in package fglrx-4-3-0
dpkg-deb: subprocess paste killed by signal (Broken pipe)
Errors were encountered while processing:
/cdrom//pool/main/x/xfree86/xlibmesa-gl_4.3.0.dfsg.1-14_i386.deb
E: Sub-process /usr/bin/dpkg returned an error code (1)
Ack! Something bad happened while installing packages. Trying to recover:
dpkg: dependency problems prevent configuration of xlibmesa-glu:
xlibmesa-glu depends on xlibmesa-gl | libgl1; however:
Package xlibmesa-gl is not installed.
Package libgl1 is not installed.
Package mesag3 which provides libgl1 is not installed.
Package xlibmesa-gl which provides libgl1 is not installed.
dpkg: error processing xlibmesa-glu (--configure):
dependency problems - leaving unconfigured
dpkg: dependency problems prevent configuration of xlibmesa-glu-dev:
xlibmesa-glu-dev depends on xlibmesa-glu (= 4.3.0.dfsg.1-14); however:
Package xlibmesa-glu is not configured yet.
dpkg: error processing xlibmesa-glu-dev (--configure):
dependency problems - leaving unconfigured
dpkg: dependency problems prevent configuration of xlibmesa-gl-dev:
xlibmesa-gl-dev depends on xlibmesa-gl (= 4.3.0.dfsg.1-14); however:
Package xlibmesa-gl is not installed.
dpkg: error processing xlibmesa-gl-dev (--configure):
dependency problems - leaving unconfigured
dpkg: dependency problems prevent configuration of libqt3-dev:
libqt3-dev depends on xlibmesa-gl-dev | libgl-dev; however:
Package xlibmesa-gl-dev is not configured yet.
Package libgl-dev is not installed.
Package xlibmesa-gl-dev which provides libgl-dev is not configured yet.
libqt3-dev depends on xlibmesa-glu-dev | libglu1-mesa-dev | libglu-dev; however:
Package xlibmesa-glu-dev is not configured yet.
Package libglu1-mesa-dev is not installed.
Package libglu-dev is not installed.
Package xlibmesa-glu-dev which provides libglu-dev is not configured yet.
dpkg: error processing libqt3-dev (--configure):
dependency problems - leaving unconfigured
Errors were encountered while processing:
xlibmesa-glu
xlibmesa-glu-dev
xlibmesa-gl-dev
libqt3-dev
Reading Package Lists... Done
Building Dependency Tree
Reading extended state information
Initializing package states... Done
Reading task descriptions... Done

This just doesn't work :|

shiva:/home/astral# apt-get -f dist-upgrade
Reading Package Lists... Done
Building Dependency Tree... Done
Correcting dependencies... Done
Calculating Upgrade... Done
The following NEW packages will be installed:
xlibmesa-gl
The following packages will be upgraded:
d4x
1 upgraded, 1 newly installed, 0 to remove and 0 not upgraded.
4 not fully installed or removed.
Need to get 0B/1479kB of archives.
After unpacking 520kB of additional disk space will be used.
Do you want to continue? [Y/n]
(Reading database ... 146158 files and directories currently installed.)
Unpacking xlibmesa-gl (from .../xlibmesa-gl_4.3.0.dfsg.1-14_i386.deb) ...
dpkg: error processing /cdrom//pool/main/x/xfree86/xlibmesa-gl_4.3.0.dfsg.1-14_i386.deb (--unpack):
trying to overwrite `/usr/X11R6/lib/libGL.so.1.2', which is also in package fglrx-4-3-0
dpkg-deb: subprocess paste killed by signal (Broken pipe)
Errors were encountered while processing:
/cdrom//pool/main/x/xfree86/xlibmesa-gl_4.3.0.dfsg.1-14_i386.deb
E: Sub-process /usr/bin/dpkg returned an error code (1)

typically if I run into a situation like that I would uninstall the offending package

apt-get remove xlibmesa-gl

then try the update again and if needed whenthe update completes you can try re-installing that package.
you may want to clear out the cached packages in the system first so it can download that package again.

apt-get clean
apt-get autoclean
apt-get update
apt-get upgrade (or apt-get dist-upgrade as the case may be)
apt-get install xlibmesa-gl (if needed since it appears the package for your ATI graphics card is supplying libGL)