1. Your strength and conditioning training should be focused on compound movements - big multi joint movements that use lots of muscles. A healthy dose of non-gym specific movements are also great for OCR athletes. Carries, throws, crawls and climbs will serve you well. The grind required to get through this type of movement is not always developed with regular exercises like Presses, Pulls and Squats.
2. Your strength and conditioning training should support your event specific training, and not detract from it.
3. Where possible you should aim to replicate the physical demands of the specific race you are competing in. Don't overthink this. You can do a lot worse than basing your training program around the actual obstacles that you'll be facing on the day. If you don't know exactly what you'll be facing then check back on previous races for a good idea.
You should never get to race day hoping that an obstacle that you are bad at comes up. If there is something that you struggle with, like Rope Climbing, then your strength and conditioning programme should prepare you for it. Adding in some Lat Pulldowns and saying "it works the same muscles" is a waste of your time. Just do some damn Rope Climbs.
4. Where necessary, supplement your strength and conditioning training with some exercises designed to support recovery and/or injury prevention. Mobility, stabilisation and flexibility training can be used to safeguard against injury.
The following workout was originally featured in Outdoor Fitness magazine in an article about Tough Mudder:
Complete 5 rounds of the following sequence:
1 Sandbag Hill Sprint (top to bottom),
10 Sandbag Thrusters,
10 Sandbag High Pulls,
10 Sandbag Chest Throws.
Use a sandbag weight that challenges you to complete all 5 rounds.