Experience: 6 years professional ff/medic, and five years in single role EMS, CrossFit (for the most part) since 2006
The short answer is that CF works very well for the fire service, and EMS as well. The problem is, you need to be careful:
My observation is that many people get injured through poor form, either by not learning the movements correctly, performing couplets and triplets that are badly paired (for example - muscle-ups or burpees with snatches), or sacrificing form to race the clock. In fact, some idiot wrote an article attempting to justify that 80% correct form is acceptable for met-cons. The other issue is that you need to ascertain the level of expertise of your CF coach. Did they do the weekend cert, and maybe a few workshops before training clients, or have they at least obtained the USAW coaching cert, perhaps traveled to Westside (like my former coach did), and have prior personal training experience, CSCS, etc.
I first found CF while researching the best way to prepare for the CPAT. I quickly identified that the O-lifts are dangerous if not taught properly. I joined an O-lifting club, and stayed with it for six months until I got hired and moved. The catch-22 is, the O-lifts are very metabolically demanding, but are also dangerous at high rep ranges. While I can get away with doing high rep OL met-cons, I find it much safer to substitute kettlebells or dumbbells for the barbell movements. For example, a double kettlebell snatch will smoke you just as much as a BB snatch. Same for the clean and jerk. Why not sub thrusters for squat cleans? Things can go horribly wrong with high-rep O-lifts. Look at the guy that just paralyzed himself doing high rep snatches. If you pay close attention to the video, as he received the bar overhead, something just gave out, sending the bar straight down onto his back. With high rep OL, something can and does give out - maybe you'll blow out a shoulder, rupture a disc in your L-spine, tear your ACL by going valgus (knees tracking inwards).
You have to be smart about your exercise selection. I see a lot of people banging their shins doing box jumps after deadlifts, squats, or jump rope in a met-con. The first jump is dicey; your legs won't work well, and you end up slicing your shins. Heavy deadlifts coupled with running is also idiotic. I'm lucky that I can deadlift over 500#, so the met-cons that call for running coupled with DL's @ 225#, 275#, 315# aren't too risky. If my max is 375, I'm at high risk for injury.
Another thing is, CF works really well for anyone at first. But after a while, you reach a point of diminished returns, chiefly due to the lack of a structured strength program. I've seen the CF games athletes doing routines totally different than the general population in the CF gym. They do regular OL and powerlifting sessions every day, maybe the gym's met-con or their own, and weakness training at another time of the day. For the long term, you can't progess in everything on 20-45 mins a day. Just look at what Rich Froning does on a typical day:
http://www.youtube.com/watch?v=f5pweLAQo_g
The good about CF for the fire service is that the work is often more intense than a typical working fire, and regular gymnsatics, OL, and kettlebell work should bullet proof your body to withstand lifting patients in position of poor leverage (pt stuck in a bathtub, between the bed and the wall, Reeves down winding stairs, etc.) in EMS. I find my firefighting duties to be easier, for the most part, than my CF workouts. Consider this: if you can get comfortable doing drills with a 2 pood kettlebell (70#), your structural PPE will feel so light, it's like you're not even wearing anything.
I recommend alternating upper and lower body strength training before the WOD (met-con) for the day, alternating lower body powerlifts first day, upper body gynastics the second, OL the third, and upper body barbell lifts the fourth. I do this over a five day cycle, doing no strength training on dayd 3 and 6, met-con only those days, off on Sun. Every fifth week I cut out the heavy lifting, but do a few extra heavy met-cons. I try to keep this schedule up to the best of my ability regarding calls and life in general, and I'm not afraid to take a day off here and there if I'm feeling a little crispy.
Here's a decent article about the pros and cons of CF. It has a few flaws, but is fairly accurate, overall:
http://www.t-nation.com/training/crossfit-the-good-bad-and-the-ugly