Pilot contamination degrades the system performance in time-division duplex (TDD) massive multiple-input multiple-output (MIMO) systems when the orthogonality among the uplink (UL) training sequences is broken. Radio front-end (RFE) impairments can contribute to the pilot contamination as well. In this paper, we study the impacts of the residual timing offsets (TOs) and the carrier frequency offsets (CFOs) on massive MIMO orthogonal frequency-division multiplexing (OFDM) systems. Particularly, we consider a TDD multi-user (MU) massive MIMO-OFDM system with either time-division multiplexed (TDM) pilots or frequency-division multiplexed (FDM) pilots. We derive closed-form expressions for the asymptotic downlink (DL) spectral efficiency in the presence of both timing and frequency errors. The results show residual TOs and CFOs destroy the orthogonality among the UL training sequences from different users and the DL spectral efficiency becomes bounded even when the number of antennas goes towards infinity. Furthermore, we propose a pilot decontamination method based on our analyses. Numerical results corroborate our analytical results and designs.