As you begin combining parts, is critical that you practice slowly. This allows your conscious mind to guide the fingers and feet through each action with security and precision until the subconscious mind is trained.
If you find persistent problems, you have probably progressed to this step too quickly. Go back to the single part or two-part combinations that still pose a challenge, deepening your learning by playing a larger number of correct repetitions than before. Do this through two or three practice sessions, and then start work on combining the three parts again later.