Formula One 04 was the first Formula One game to contain a 'Career mode', which allowed players to work their way through the Formula One teams over the course of five years (albeit a repeat version of the 2004 season each time). Players would start out testing in a generic Formula One car, and if they did well enough in the test they would be offered a contract by a small team such as Minardi. Players would then work their way up the grid throughout their 'career' through a mixture of good tests and impressive race performances. This game also had Net Play available.
This is the only F1 game in the series to be changed in terms of gameplay after the original release. In the original version, there was a bug which when during the timing of AI pitstops all the field crawled at pit lane speed, then they sped up once a few of the AI cars had made their stop, and it was very common to be following a car which suddenly came to a halt and you would end up hitting their rear and ending your race. Studio Liverpool responded to the fans concerns about this issue and fixed this glitch upon the release of the Platinum version. Another criticism is that the field rarely overtakes another car.
Source: Wikipedia, "Formula One 04", available under the CC-BY-SA License.