As the chainsaw pierces the windscreen of the car, a bracket is visible on the tip of the saw. In the next shot it is no longer present.
Smoke Jumpers do not jump with their tools, these are delivered in separate cargo parachute drops.
Jennifer tells Jessie that she is a former US Marine Corps medic - in actuality the Marines have no medical personnel and rely upon the Navy to provide medical corpsmen.
Jesse throws the chainsaw at the car with the chain running. Safeties on the saw would not allow the chain to continue to run without an operator holding it.
When Jessie and Jennifer parachute together, a cable can be seen holding her to him.