I recently discovered that VNC on Debian Wheezy is a bit of a mess.
VNC can be used in two modes: to mirror the actively running instance of X (i.e. the display on :0), or to have X running headless, in any resolution ("geometry") you want, on :1, :2, etc.
The version that comes with Wheezy by default, is an old version of TightVNC server. It doesn't support the alpha channel, so modern desktops like KDE 4 will look pretty bad.
Development has stopped on TightVNC, and continues in the TigerVNC project. There are packages available here, but these are pretty old now: version 1.1, while development has passed 1.3.
In and of itself that wouldn't be a problem, except the 1.1 version has a horrible bug where moving a window to the left will result in display artifacts.
You may also have found TurboVNC. Development seems to move slower but they do provide Debian packages. Unfortunately, even for the latest version it seems it suffers from the same bug.
There's a couple of options:
I'm currently looking at other solutions such as X2Go, which seems to provide decent packages.
Edit 2014-08-26: For the last two months or so, I started using the standard VNC again, and I've switched to XFCE as the desktop environment. This solves most problems, except you run into an easily fixable bug: the tab key doesn't work to auto-complete. This link
solves the problem.