I'd use the first part of Corion's answer and combine it with LanX's answer (see above).
In other words, use Text::CSV_XS and use placeholders, but keep the RaiseError flag on and use it to jump out of an eval block. There, write away the failing incoming input-line into a separate .reject file, so that you can later review the rejected lines. Also count the total number of input-lines, good lines and bad lines so that at the end you can output a status line, so you'll know what has happened.
(COPY will be much faster but it is fickle and will fail outright when you have ANY bad input lines, even flagged CSV will fail. You could try it one time: if it does not fail, you have the speed; if it does fail, you redo by using the insert line-per-line, as explained above)