Here is a physical problem: Knee injury from sitting postures without requisite hip flexibility. This applies to almost any floor-sitting posture, depending on the meditator's hip flexibility. This is based on my own experience injuring my knees in sitting meditation.
The knee injury occurs when insufficient hip flexibility causes the knee joint to rotate laterally. Lateral, in anatomical terms, means away from the body in a left/right direction.
The knee is a very simple joint mechanically, and is only designed to flex and extend. It is damaged by rotating medially/laterally. The lateral rotation required for sitting postures should come from the hip.
Full lotus position (each foot on top of opposite thigh) and half lotus position (one foot on top of opposite thigh) are the most dangerous positions for this case since they cause a lot of lateral rotation in the knees, if there is not sufficient hip flexibility. Burmese position (one foot in front of opposite shin) is much less dangerous, but might still injure a person with tight hip ligaments.
So the key is that we need flexible hips if we want to sit on the floor easily.
Although full lotus and half lotus position are discussed more in Yoga, and not in the context of Buddhist meditation, I feel this advice still applies since I injured my knees by sitting in half lotus. Now I protect my knees by avoiding lateral rotation, keeping my hips flexible, and only using Burmese position for sitting.
This video by KinoYoga shows how to prepare for lotus position safely, and can help to clarify by providing visual instruction.
And this page has many stretches I have found useful to loosen the hip for safer sitting:
Be well and take care of your knees.