One problem related to engine has been reported for the 2004 Mazda MX5. The most recently reported issues are listed below.
Car would not accelerate. I came to a stop at a toll booth. When I went to pull away the car would hardly accelerate. Any amount of throttle would cause the car to bog out. Seems very likely a crash could occur if this problem happened at the wrong time. This is specifically a problem with the Mazdaspeed model of the mx-5.