The narrowest and most interesting way to interpret your question is that you want anecdotes exemplifying language-based misunderstandings between ancient individuals; like, if Caesar said "Ave" and Cleopatra thought he was talking about birds. Sadly I'm not aware of any such anecdotes myself.
Interpreting the question broadly, there are literally hundreds of examples of scholars holding incorrect beliefs based on coincidental similarities of pronunciation between words in different languages. I'm thinking of false etymologies. The Wikipedia page on folk etymology lists many examples from all kinds of languages, but most notably
the word baceler or bacheler ... referred to a junior knight. It is attested from the eleventh century, though its ultimate origin is uncertain. By the late Middle Ages its meaning was extended to the holder of a university degree inferior to master or doctor. This was later re-spelled baccalaureus, probably reflecting a false derivation from bacca laurea "laurel berry" ...
Also, an intra-Latin example:
sincere is derived from the Latin sincerus ... from sin- (one) and crescere (to grow) ... An often repeated folk etymology proposes that sincere is derived from the Latin sine (without), cera (wax). According to one popular explanation, dishonest sculptors in Rome or Greece would cover flaws in their work with wax to deceive the viewer; therefore, a sculpture "without wax" would mean honesty in its perfection. ... Another explanation is that this etymology "is derived from a Greeks-bearing-gifts story of deceit and betrayal. For the feat of victory, the Romans demanded the handing over of obligatory tributes. Following bad advice, the Greeks resorted to some faux-marble statues made of wax, which they offered as tribute. These promptly melted in the warm Greek sun." The Oxford English Dictionary states, however, that "there is no probability in the old explanation from sine cera 'without wax'".
Finally, for a perennial case of cultural confusion between a Scandinavian-derived word and a similar-sounding Latin-derived word, look no further than niggardly.