I wish I had gotten a cent whenever this technique was done wrong by someone. I wish I had a dollar for every source that depicts that technique wrong.
The biggest problem with Tani Otoshi is, that even done in a wrong, non-traditional way, it still has a high success rate. That's why we see even olympionites doing and teaching it in dangerously incorrect ways.
Tani Otoshi is one of the most misunderstood techniques in Judo and dangerously so.
The idea of Tani Otoshi is, that tori sits down into the direction of the throw, which is towards the back of uke. It doesn't matter if he sits into it looking into the direction of the throw, sideways or with his back towards the throwing direction. To do so safely, tori extends his leg while he sits down. Only then he draws uke down to the ground.
Under no circumstances tori may try to block, sweep or reap uke's legs, neither the one closer to him, nor the other one. He may not hang himself with his weight into uke and try to plant his leg for blocking. He may not try to put it in the back of either knee and he may not drive his weight from any direction into uke's knees and he may not sit on uke's foot and/or add a twisting motion to the throw.
All of the above are common mistakes! Many of them are even taught by high ranking teachers as the correct form, which can have terrible consequences.
Let me illustrate the dangers with examples:
Black belt demo! Second attempt almost ends with leg injury:
https://www.youtube.com/watch?v=zneJQlH-eOo
Here the same mistake in competition, even worse, tori shoves his mass sideways into the knee:
https://www.youtube.com/watch?v=RiMrQPnWILs
If tori drives his weight into uke's offsite ankle, it may happen that uke's foot is not sufficently separated from the mat and gets caught. This results in ligament damage:
https://youtu.be/ySwG_QN6Mg4?t=1m26s
When Tori's leg is positioned in the back of uke's knee as it bents, this puts great stress on the joint and pulls it apart. I had a clip of that from an international competition, but it was deleted from Youtube.
Here tori turn-slides closely behind uke's legs and damages them:
https://www.youtube.com/watch?v=XrH0fGPoOb0
I was witness to an accident where tori slid into the offside leg in training, ending with ligature damage.
A member of r/judo reported how tori placed the knee in the back of his knee, where the leg got caught, but instead of destroying his knee when he fell, he fell onto tori's caught leg, breaking it in 3(!) places.
This is how it is done correctly without leg contact:
https://www.youtube.com/watch?v=B166K9X-wDA