This paper presents non-linear precoding design in closed-loop multiple-input multiple-output (MIMO) orthogonal frequency-division multiplexing (OFDM) over spatially- correlated, frequency-selective fading channels. Our analysis takes into consideration receiver channel mismatch due to imperfect channel estimates, and transmitter channel mismatch due to estimation errors, channel variations over feedback delay and feedback noise. We present a general spatially-correlated, frequency-selective fading MIMO channel model and derive the conditional means of the channel response. Exploiting the channel statistics, which are only available at the receiver, we design new non-linear zero-forcing (ZF) Tomlinson-Harashima precoding (THP) for uncoded MIMO OFDM. The channel statistics do not need to be sent back to the transmitter, which avoids the possible maximum-Doppler-shift transmitter mismatch. Our proposed precoders are robust against time variations, channel estimation errors and antenna correlations, and offer a significant system performance gain over conventional THP.