I've been curious about crossfit, and checked out crossfit.com. In their "start here!" article they point out that beginners and people not all that fit should take their time to build strength and technique before attempting the most demanding exercises.
I'm a big fan of low tech training because not being strapped inside a machine that isolates on one specific muscle group means that you activate a whole bunch of muscles required to stabilize and support the muscles that does the actual work.
I like the crossfit philosophy, but frankly I think their regime is most suited to people who are quite overall fit to begin with. People that are not so fit must adjust technique and intensity. Less fit means larger adjustments. Which is fine for some, but it does require some insight (finding substitute movements, listening to your body signals and so on). And always falling WAY behind those ultrafit cult members may be very demotivating.
One pitfall would be starting too hard: Too heavy weights, too high intensity for your own level, and not allowing for sufficient time to perfect your technique. All of which are great recipies for injuries.
If you have the mental tools for dealing with the above challenges I'd say go ahead and try it - it does sound like fun.
Not having a crossfit in my immediate neighborhood I stick with my local gym and their interval training - which is a much more limited set of excercises (burpees, plank, squat and so on) done at high intensity. Each exercise is done for a certain time period (30 or 60 seconds) before swapping to the next, no break untill you've done all the exercises in a cycle. Two minutes break, repeat. And repeat. Great overall training: Strength, cardio, coordination... For me it really has done wonders