Patch with COPY FROM errors handling seems to be quite finished, so I have started thinking about parallelism in COPY FROM, which is the next point in my proposal.
In order to understand are there any expensive calls in COPY, which can be executed in parallel, I did a small research. First, please, find flame graph of the most expensive copy.c calls during the 'COPY FROM file' attached (copy_from.svg). It reveals, that inevitably serial operations like CopyReadLine (<15%), heap_multi_insert (~15%) take less than 50% of time in summary, while remaining operations like heap_form_tuple and multiple checks inside NextCopyFrom probably can be executed well in parallel.
Second, I have compared an execution time of 'COPY FROM a single large file (~300 MB, 50000000 lines)' vs. 'COPY FROM four equal parts of the original file executed in the four parallel processes'. Though it is a very rough test, it helps to obtain an overall estimation:
Serial: real 0m56.571s user 0m0.005s sys 0m0.006s
Parallel (x4): real 0m22.542s user 0m0.015s sys 0m0.018s
Thus, it results in a ~60% performance boost per each x2 multiplication of parallel processes, which is consistent with the initial estimation.
the important use case is big table with lot of indexes. Did you test similar case?