Synecdoche as I've most commonly encountered it in various Bible classes was the use of a part to reference the whole (as hand for sailor), but according to American Heritage Dictionary, it can also refer to: the whole for a part (as the law for police officer), the specific for the general (as cutthroat for assassin), the general for the specific (as thief for pickpocket), or the material for the thing made from it (as steel for sword).
Last week I referred to the Mechilta what explained that Moshe did not originally judge alone, but based on the words Gam Ata, Gam Et HaAm HaZeh, there were also Aharon, optionally Nadav and Avihu, plus 70 elders who judged with him, before Yitro's suggestion of adding judges. They darshened this as follows: Ata was Moshe. Gam was Aharon or Aharon + Nadav and Avihu. HaAm was the elders. This even though pashut pshat seems to be that HaAm refers to the people who wanted to be judged by Moshe and not the elders who were doing judging.
However, as I read further, it seems that indeed we may be dealing with synecdoche, in this case with the whole - the Am being used to refer to the part - the elders of the Am. Two proofs:
1) Towards the end of Mishpatim, after listing the laws, we have the following instruction (Shemot 24:1-2):
"And to Moshe He said, 'Ascend to Hashem, you and Aharon, Nadav and Avihu and seventy of the elders of Israel, and bow from afar.' And Moshe alone approached Hashem and they did not approach, and the Am did not ascend with him."
The first pasuk lists the parties we saw earlier in the midrash- Moshe, Aharon, Nadav, Avihu, and the elders. (We see them again in pasuk 9.) In the second pasuk, we have Moshe, "they," and the "Am." Why should the nation be listed as not going up - after all, the command referenced only Aharon, Nadav, Avihu and the elders. I would suggest that perhaps "they" refers to Aharon, Nadav and Avihu, and the Am refers to the elders of the Am.
2) In last week's parsha, Yisro, in Shemot 19:7 we read:
"Moshe came and called to the elders of the Am and placed before them all these matters which Hashem commanded him."
Yet in the next pasuk:
"And all the Am answered together, saying that Hashem says we will do, and Moshe brought back the words of the Am to Hashem."
Where did the Am come from is Moshe spoke to the elders of the Am. Midrashim and meforshim deal with it, but perhaps there is nothing to deal with, for when the Am answered, what is meant is the elders of the Am, and we are dealing once again with a synecdoche.