The risk is that stuff will randomly not work, and you will have no idea why.
Hypothetically desktops should be able to share a system, and developers should ensure that having one desktop installed does not interfere with another. The problems appear when desktops rely on different software to implement the same services, and the developers of both desktops just say "well, it works on our desktop, you should just remove the other desktop".
One example: bug #984230 - the packages xfce4-notifyd (from XFCE) and notify-osd (from Gnome/Unity) are incompatible, and if you install XFCE and Unity at the same time, you will find that notifications in XFCE do not work as expected, because the notification service is activated by DBUS, and notify-osd always gets run instead of the XFCE version. notify-osd developers do not consider this a bug in notify-osd, and xfce4-notifyd developers do not consider this a bug in xfce4-notifyd, since both work fine when the other is not installed!
Another example: bug #889394 - having gnome-screensaver, xscreensaver and xfce4-power-manager installed at the same time. They both had the same timeout. The result of this was that after some time, one screensaver kicked in and turned off the monitor (dpms), but the other would just black the screen (no power off). So depending what order they got run, which was essentially random, the monitors would either stay on or turn off. One of the confusing thing about this situation was that both screensaver applications have different settings, so changing settings can result in no effect on what is actually happening.
Another confusing thing is that XFCE will try to lock the screen using xflock4, but it will always use xscreensaver if it is present, never gnome-screensaver, and you have no way of knowing this unless you look at the source code. And xubuntu-desktop depends on both xscreensaver and xfce4-power-manager, even though they conflict.
So, that is why I try to avoid installing more than one desktop, and instead install each desktop with its own full install on a different partition. You can install more than one desktop on the same system, but the developers of each desktop are less likely to care or fix bugs that only occur when two or more desktops are installed.
Some more incompatibilities to watch out for: