For Greek and Latin texts, translations certainly can be out of date. There are several reasons for this.

First, the reconstruction of the text in the original language changes over time. Those changes might be based on something like new finds of papyri or manuscripts that provide alternative readings or confirm what might have been a minority opinion based on previous evidence. Editing the original text obviously will change how that text is translated. If you are interested in textual criticism (the process by which we reconstruct ancient texts) I will point you to this bit of the FAQ.

There are also... I'm going to say fads for lack of a better word... of translation that fall out of use. One example would be Bowdlerization, the practice of leaving "unseemly" text untranslated, or translated into another language rather than the target language, or omitted all together. That was common in the 1800s and the early 1900s. I was still reading Bowlderized translations when I was in college in the early 2000s, and let me tell you it fucks with Roman poetry. What are you going to do with a translation of Catullus that doesn't print poem 16?

There is also the trend to render the translation of a Latin or Greek poem into something the English ear recognizes as poetry, like rhyming couplets or something. For instance, the beginning of Alexander Pope's 1700-something translation of the Iliad:

The wrath of Peleus' son, the direful spring

Of all the Grecian woes, O Goddess, sing!

That wrath which hurled to Pluto's gloomy reign

The souls of mighty chiefs untimely slain,

Whose limbs, unburied on the naked shore,

Devouring dogs and hungry vultures tore:

Since great Achilles and Atrides strove,

Such was the sovereign doom, and such the will of Jove!

The idea is to preserve the sense of poetry (such as it is) rather than translate the text faithfully to the grammar and meaning.

My translation of the same stanza from the OCT is in prose:

Rage! sing, goddess, the accursed rage of Achilles, son of Peleus, which brought incalculable pain to the Achaeans. It sent many strong souls of heroes to Hades, and made them prey for all the dogs and birds, and accomplished the will of Zeus. Sing from when they first stood apart and quarrelled, Atreides Lord of Men and the divine Achilles.

Apologies for my rusty Greek. I think my translation is closer to the sense and grammar of the Greek, but lacks the poetic form of Pope's.

There is also a habit of trying to provide a translation in "updated" language. I especially despise this. I recall reading the phrase "Tom, Dick, and Harry" in a translation of Juvenal. The intent was to render three mostly anonymous yet stereotypical characters into an English phrase the reader would understand right away, but it's perfectly clear those are ENGLISH characters, not Roman ones. Using that kind of phrase imports a whole different cultural understanding into the translation. This can get so extreme that we have Biblical paraphrases that focus so much on modern phrasing they completely forget the grammar and rhetoric of the original.

More recent translations are usually published because something has come to light pointing out an older translation is deficient in some way. That can be new evidence, but it can also be a new perspective on the original text. Emily Wilson recently translated the Odyssey, apparently the first woman to have published such a translation. I have not read her translation yet, but the reviews speak of a female translator's perspective bringing new meaning to the text in which women play pivotal and controversial roles.

When you're looking at a translation, you want to consider what version of the original text you're looking at, whether the translator is interested in accuracy or "feel" for lack of a better word, whether the translator has moral qualms about the text, and whether "updated language" is an issue for them. Also consider the voice of the translator, as different translators are interested in different things, and not all of those things serve your purposes.

AND I've run out of thoughts, so I'll just sign off now. Bye!