The biggest American mistake was in the withdrawal from Lebanon after the 241 Marines were killed in a truck bombing.
The message of weakness and stupidity that was given to the entire Arab world is going to keep costing our children and grandchildren plenty. Tribes that have been in conflicts and feuds for decades to centuries have zero respect for someone who will not stand their ground. They look at the 241 men out of 280 million Americans (at that time) and very properly consider it a mere pinprick.
I regard that as one of the most costly basic errors of the past few centuries, like the decision to bomb Pearl Harbor.