The performance of multicarrier systems is highly impaired by intercarrier interference (ICI) due to frequency synchronization errors at the receiver and by intermodulation distortion (IMD) introduced by a nonlinear amplifier (NLA) at the transmitter. In this paper, we evaluate the bit-error rate (BER) of multicarrier direct-sequence code-division multiple-access (MC-DS-CDMA) downlink systems subject to these impairments in frequency-selective Rayleigh fading channels, assuming quadrature amplitude modulation (QAM). The analytical findings allow to establish the sensitivity of MC-DS-CDMA systems to carrier frequency offset (CFO) and NLA distortions, to identify the maximum CFO that is tolerable at the receiver side in different scenarios, and to find out the optimum value of the NLA output power backoff for a given CFO. Simulation results show that the approximated analysis is quite accurate in several conditions.