Please note that the techniques summarised below may not necessarily be identical or capture all that was taught in class.
Nage-waza (throwing technique):
Tai otoshi (body drop) is classified as a te-waza or hand technique. Consequently, applying an effective tai otoshi can be challenging if one applies mechanical principles from other forward throws such as hip throws (koshi waza). A good written instructional on common tai otoshi errors can be found on this blog, which touches on several topics covered in class:
Nicholas Gill, Canadian Olympic medallist, demonstrates the difference between good and bad weight distribution between legs, in terms of spacing between tori and uke and concomitant ability to apply pushing power with the arms.
The posture for tai otoshi is fairly straight upwards. A bent posture tends to throw weight distribution off and/or disrupt arm action, which sometimes leads people to try wraparound sacrifice throws (makikomi) to salvage their entry.
Distancing between tori and uke
Unlike hip throws, there is space between the hips and torso of tori and uke in tai otoshi. You may hear this idea being called body management (tai sabaki), which can be different for different techniques. Good tai otoshi body management fits together with good weight distribution and posture.
Finally, the Kodokan video on tai otoshi: