1. How could such a mistake have occurred between the two teams?

NASA designed the Mars Climate Orbiter spacecraft to collect data about Mars’ atmospheric conditions and serve as a data relay station. Instruments aboard the Orbiter would provide detailed information about the temperature, dust, water vapor, and carbon dioxide in Mars’ atmosphere for approximately 2 Earth years. The Orbiter would also provide a relay point for data transmissions to and from spacecraft on the surface of Mars for up to 5 years.
Nine months after launch, the Orbiter arrived in the vicinity of Mars and fired its main engine to go into orbit around the planet. Everything looked normal as it passed behind Mars as seen from the Earth. After that, the Orbiter was never heard from again; presumably it had crashed into the planet. Paraphrasing project manager Richard Cook, “We had planned to approach the planet at an altitude of about 150 kilometers, but upon review of data leading up to the arrival, we saw indications that the approach altitude was much lower, about 60 kilometers. We believe the minimum survivable altitude for the spacecraft would have been 85 kilometers.”