The flight crew's continued descent of the airplane below the glideslope and through the published decision height without visual contact with the runway environment. Also, when the captain encountered difficulty tracking the localizer course, his improper decision to continue the approach by transferring control to the first officer instead of executing a missed approach contributed to the cause. In addition, the following were factors to the accident: (1) American Corporate Aviation's failure to provide an airworthy airplane to the flight crew following maintenance, resulting in a false glideslope indication to the first officer; (2) the flight crew's failure to follow company crew coordination procedures, which called for approach briefings and altitude callouts; and (3) the lack of an FAA requirement for a ground proximity warning system on the airplane.