This paper deals with the effects of residual timing and frequency offsets on the symbol error rate (SER) performance of an orthogonal frequency division multiplexing (OFDM) system. The synchronization of an OFDM system generally consists of a coarse frequency and timing acquisition stage and a refine stage. Due to the presence of Gaussian noise, channel distortions and implementation losses of synchronization and equalization algorithms, residual frequency and timing offsets always exist for an OFDM receiver. The residual frequency and timing offsets are proven to be Gaussian distributed, with their corresponding variances determined. The reception process of an OFDM signal with frequency and timing offsets is analyzed. A closed-form analytical result on the SER of an OFDM system with residual synchronization errors is derived. Computer simulations and analyses show that the frequency and timing offsets affect the OFDM subcarriers differently. With this observation, a new technique is proposed to minimize the SER of the OFDM systems by adjusting the distribution of transmission power among the subcarriers.