Just to note, a 1st edition of the Illiad would certainly be of one of the translations. The 1951 translation by Richmond Lattimore seems the most plausible — old enough to be found at a garage sale, not so old that it would be totally ridiculous. The style of the book in the movie doesn’t necessarily match that, but it also doesn’t match a 1720 AD first edition of Alexander Pope’s translation.
From what I can find (thank you, Google), Richmond Lattimore’s version is considered one of the essential versions, and preferred by many.
The translations of classic works of poetry are considered classics in their own right. It takes a great poet to translate not only the words of a poem, but infuse them with a sense of poetry.
All that to say, while the acting in that scene seems clunky and awful, and finding the 1st edition for a buck at a garage sale is unlikely (though I’ll grant I’ve heard stories like that in real life), the actual question of it being a 1st edition is not in reference to the Illiad, but to the particular translation, and is not ridiculous at all.