A considerable amount of longitudinal play becomes apparent in the towing device of the trailer. What effect can this have?

You answered correctly. If the towing device of the trailer has too much longitudinal play, it means there is excessive movement where the trailer connects to the towing vehicle. This can lead to two problems: first, damage to the cross beam of the towing vehicle because of the repeated shocks and forces during driving; second, in extreme cases, the trailer could shear off, meaning it could detach from the towing vehicle entirely. Both are dangerous and must be avoided by keeping the towing connection in good condition. Overloading the rear axle tyres, however, is not directly related to this issue. Always ensure the towing device is secure to prevent these risks.