When experiencing a rough idle in your 2013 BMW 750Li, it's essential to consider several common problems that could be at play. One of the primary culprits is a vacuum leak, which can disrupt the air-fuel mixture and lead to an unstable idle. Additionally, worn or faulty spark plugs can cause misfiring, resulting in an uneven engine performance. Ignition coil issues may also contribute to this problem, as they are crucial for proper spark generation. Another component to inspect is the Idle Control Valve (ICV); if it becomes dirty or malfunctions, it can fail to regulate the idle speed effectively. Furthermore, disruptions in the engine's combustion process, potentially due to clogged fuel injectors, can exacerbate rough idling. Lastly, if your vehicle is equipped with the N63 engine, be aware that it may exhibit rough idle symptoms alongside poor acceleration and black exhaust tips, indicating unburnt fuel. By addressing these issues promptly, you can enhance your driving experience and maintain the performance of your BMW 750Li.