The GUI on Linux, like most Unix-like operating systems, is based on the X11 protocol and its server/client model. The protocol has been around for a long time, and standardizes a lot of interesting features like network transparency (so you can run applications on another computer with the windows being drawn on your workstation), but it also lacks in a lot of areas that didn't matter when it was created (3D graphics, display hotplugging and live reconfiguration, changing screen resolutions, screen rotation and multiple monitor support, etc.). As such, a lot of extensions have cropped up over the years to handle these features.
The first real gotcha to watch out for is with dual displays. In the past, you used to use multiple graphics cards hooked up to different screens and the Xinerama extension. Nowadays, you use Xrandr with any video card that supports dual-head, and you change you screen settings using the xrandr command. Most of the open source video drivers that support Xrandr only have accelerated 2D graphics though, so unless you're using an older ATI Radeon card, you'll want to use proprietary drivers for 3D. If you have an NVidia card or an ATI card, you use their proprietary drivers and NVidia's "Twinview" or ATI's "MergedFB" extensions for dual display setup.
However, the problem with Twinview and MergedFB is that you can't load individual ICC profiles for each screen, so if you have a screen calibration tool and make custom color profiles like I do, then you'll have to use Xrandr with either an ATI card with the open source drivers for lower-performance 3D accelerated graphics, or stick to 2D graphics. Otherwise, you'll only be able to have one screen calibrated at a time.
The other thing to watch out for with dual-display setups is getting wacom graphics tablets to work correctly. Some of the options don't work as documented -- you can just set the tablet to work with one screen, but usually whichever screen is detected as screen 0 will be the one it works on. However, there's a lot of room for bugs to occur.
I had Xinerama set up with NVidia's drivers in Ubuntu so I could load ICC profiles (at the cost of no 3D graphics), and no matter what I did, the tablet would draw on half of one screen and then half of the other, skipping the center halves of both screens, but drawing in the GIMP worked as though the tablet's area were stretched over both screens, making the brush appear at a different point from the cursor.
However, as the Xrandr extension becomes the standard way of doing things, and proprietary drivers begin to implement either Xrandr or some of its color management features, these problems should disappear.
If you use wacom tablets, another gotcha to watch out for if you use anything other than Ubuntu is a resolution bug between the X11 display server and the wacom driver. This stuck around all of last year, since very few programmers and distro maintainers had any clue how tablets were supposed to work, or what kind of quality users were supposed to get in the GIMP, so when things broke and everyone started getting really wavy lines with the GIMP's ink tool, they assumed that's the way it worked and told people to just zoom in to 200% to get smooth lines. Later it turned out that the bug was due to conflicting assumptions and changes between the X.org X11 display server and the linuxwacom drivers concerning the XInput extension that made all tablets super-low resolution, killing everyone's line quality. The only distro to include patched drivers was Ubuntu, so pretty much every 2008 version of every other distro has broken wacom tablet support.
If you stick to one screen and don't use a drawing tablet though, you should have an easy time, especially with Ubuntu. If you have a color calibration tool like the huey Pro or a Sypder, you can even do color management using Argyll CMS.
