Double Speed Operation for USART on Arduino Mega 2560
When in double-speed mode, as noted in the manual, fewer samples are used. In Asynchronous serial communication, there is no clock signal, so the clock that keeps the two devices in sync is extrapolated from the data signal. Each end of the communication has it's own clock source (crystal oscillator, ceramic resonator, R-C oscillator, etc.), and you'll rarely find two that are calibrated identically. 

The receiver samples the signal at a higher rate than the actual baud rate so that it can better determine where, relative to it's own clock, the data-signal edges go up or down and continually adjusts its offset to compensate for clock drift.

By operating in double-speed mode, the receiver has fewer samples to work with, and so if your transmitter has a clock source that is different enough than the receiver, or is not stable, or you have long or noisy wires or fluctuating temperatures (etc.) then you may experience less stable communication.

If your particular use-case works fine, then stick with it. But if you start to notice errors in communication, the first troubleshooting step would be to disable this mode, since the clock recover is less robust in this mode.