Since no one's responded, yet, I'll throw my two cents in...
Mobility wod is great. The dude's a genius. Buy his book "Becoming A supple leopard". You can do ALOT with a lacrosse ball, and you don't have to spend a bunch of money (like I did, but still worth it) on the mobility equipment. For hip mobility, check out "HAM hip mobility" and "HUG hip mobility" drills on youtube. These were put together by rob shaul and were designed to be done during a workout, our during a dynamic warmup.
For warmups, here is great advice from the "SOFWODs" website. I try to follow this as best as possible. They do similar training to OMOB, although typically longer in duration for the endurance and metcon training portions...
"Conduct the SOF WODs Warm Up prior to every WOD:
5+ minutes on a foam roller
400m Run or Row
20 push ups
20 sit ups
20 air squats
20 back arches
Hang on the pull up bar to elongate spine and open shoulder capsules.
3 x 5 pull ups
Dynamic stretches (stretches involving movement)
Static stretches (stretches with limited movement)
Work on specific movements with PVC or a 45# bar
- Post WOD conduct 10+ minutes of stretching and a 5+ minute flush on the foam roller. Reference www.mobilitywod.com for pointers on mobility."
Edit: forgot to answer your question about core strength. Generally, with cross-fit/strength workouts you should be engaging your core with pretty much every single movement. I believe Ground Zero specifies core strength in order to develop the core of those who haven't been on a regular workout program in a while. With that said, the only core exercise I'll be doing is keepin it tight during the strength portions, and during the WODs.