Actually, when it comes to compare bibles from different times periods, copying mistakes are really rare. When a book is afoundement of an entiere religion (if not civilisation), copies tend to be watched carefully.
I on't speak arameic or ancient greek so won't pretend to be an expert but simply look at the difference in terms used for the same passage in various version (I picked a fairly straightforward one and one that is relevant):
Corinthian 6: 9-10
English Standard Bible
9 Or do you not know that the unrighteous will not inherit the kingdom of God? Do not be deceived: neither the sexually immoral, nor idolaters, nor adulterers, nor men who practice homosexuality,
10 nor thieves, nor the greedy, nor drunkards, nor revilers, nor swindlers will inherit the kingdom of God.
King James bible
9 Know ye not that the unrighteous shall not inherit the kingdom of God? Be not deceived: neither fornicators, nor idolaters, nor adulterers, nor effeminate, nor abusers of themselves with mankind,
10 Nor thieves, nor covetous, nor drunkards, nor revilers, nor extortioners, shall inherit the kingdom of God.
Catholic Bible
9 Do you not realise that people who do evil will never inherit the kingdom of God? Make no mistake -- the sexually immoral, idolaters, adulterers, the self-indulgent, sodomites,
10 thieves, misers, drunkards, slanderers and swindlers, none of these will inherit the kingdom of God.
Geneva Bible (1599)
9 Know ye not that the unrighteous shall not inherit the kingdom of God? [a]Be not deceived: neither fornicators, nor idolaters, nor adulterers, nor wantons, nor buggerers,
10 Nor thieves, nor covetous, nor drunkards, nor railers, nor extortioners shall inherit the kingdom of God.
La Bible du Semeur
9 Ne savez-vous pas que ceux qui pratiquent l'injustice n'auront aucune part au *royaume de Dieu? Ne vous y trompez pas: il n'y aura point de part dans l'héritage de ce royaume pour les débauchés, les idolâtres, les adultères, les pervers ou les homosexuels,
10 ni pour les voleurs, les avares, pas plus que pour les ivrognes, les calomniateurs ou les malhonnêtes.
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Now the first one makes it pretty clearly that gay sex is wrong, in the second it can be *assumed* so (modern people could take effeminate as being a coward). The catholic bible makes a bit murkier since "sodomites" was an historical term meaning gays but could also mean someone practicing sodomy (just like in the geneva bible) meaning that people having "unnatural sexual acts" (in the old sense) or anal sex (in the modern sense) would be denied heaven even if said unnatural act was not committed between people of the same gender.
You'll also appreciate that in the french version I included it's gays *and* perverts that get the shaft so even without straight up mistake (such as "les chaussures de vair" becoming "les chaussures de verres") you still have a bias in translation. add the old testament text in which figure of speech might be lost and you got a recipe for disaster.