Confusion about the impact of flat fading and frequency selective fading on OFDM OFDM divides the signal in frequency domain into orthogonal and relatively narrow subcarriers where fading can be considered to be flat
Flat fading is not associated with delay spread and is corrected in frequency domain

Delay spread caused by multipath is associated with frequency selective fading and in OFDM it is absorbed by the cyclic prefix which isolates consecutive OFDM symbols

How would delay spread show up in the frequency response of the channel? would it show up like "nonflat" fading or a notch within the relatively small bandwidth of some subcarriers?

i.e. it would be wrong in this case to consider the affected subcarriers still experiencing flat fading?
Because of wide-band nature of OFDM signals they are so prone and sensitive to multi-path delayed channel. The problem is that at the receiver side you will receive several copies of original transmitted signal, each with a different magnitude and delay. This "delays" are so destructive at the receiver side. The mathematics behind this: imagine the channel with multi-path problem. so u can model this channel as a linear-system with an "impulse response". this impulse response consists of several impulses with different magnitude and delays. so, your sent OFDM signal passes through this channel. the result can be guessed. at the output this system, the OFDM signal is convolved with the impulse response of the channel (system) in time domain. In frequency, it is like as the freq-domain OFDM signal is multiplied by the frequency-response of the channel. That's why we face a distorted received signal. At the receiver, when you apply FFT on the received signal you have to compensate that errors. This is called channel estimation (means estimating the freq-response of the channel). Then you should correct the signal. This is so crucial because in OFDM we usually have QAM modulation &amp; demodulation. and in QAM the magnitude of signal is important which is already distorted by the channel.