Flat spot has two automotive meanings, one relating to engine performance and the other to tyres.
An engine flat spot is an operating condition where the engine response is poor. Often the term indicates a point near the middle of the engine speed range where strong and immediate engine response dies away, before returning as the engine accelerates to a higher speed. This kind of flat spot can be caused by poor fuel or ignition mapping, amongst many other factors.
In motor racing, flat spot can refer to tyre damage which is often caused by locking a brake (above). This causes the tyre to wear away in one spot around the circumference. The resulting vibration is uncomfortable for the driver, reduces grip and in extreme cases can lead to suspension failure (as happened to Kimi Raikkonen's McLaren at the German GP in 2005).