In ancient texts it happens a lot more than you probably expect. All manuscripts are corrupted, without exception. These are hand-copied manuscripts, and even in antiquity texts were getting corrupted by copyist errors--these errors only became more common in the Middle Ages, especially as proficiency in the classical languages decreased, meaning that often monks would think that something they were copying was syntactically impossible when in fact it was just something they weren't familiar with (just as one example). There's an entire field of study, textual criticism, on figuring out what the manuscripts actually say. Generally textual critics use different manuscripts of the same text (since we often have several different copies) and compare them with each other to find a consensus. I'll spare you the gory details, but that's usually a pretty good way to work out corruptions in the text. Sometimes, though, it doesn't work. Either we only have one or a handful of copies of a text, or sometimes all or most of our texts have a reading that we know (or suspect) must be wrong. Sometimes (as is often the case with, say, Propertius) all the possible readings are wrong or don't seem to make sense. In cases like these the textual critic has to make a conjecture of his own. Again, I'll spare you the gory details but there's lots of methods that textual critics can use to work out disputed readings, from known patterns of orthography (words that looked similar were often mistaken for each other) to conjecture that marginal notes were incorporated into the text (which happened with alarming frequency--luckily it's usually patently obvious).

Generally the texts that we work with have already been dealt with by textual critics, we don't deal with the unedited manuscripts. In the event that we find a reading that we find is fishy, editions will provide an apparatus criticus, which is basically a collection of all the places where the editor chose a reading and his reasons for doing so. From there if we think the editor is full of it we can pick some alternate reading he's rejected. Usually that doesn't happen--more often causes for uncertainty in our ancient texts are ones of semantic meaning rather than disputed readings in the manuscript. There are a very few examples where problems like this occur with slightly greater frequency. First is names. Names get corrupted decently often, and often the copyists didn't actually know who the hell these people were, misspelling names and making other errors. You may be familiar with a centurion by the name of Titus Pullo, who served under Caesar's legate Quintus Cicero (the orator's brother) against the Nervii and later defected to Pompey--he features as a highly-fictionalized (he doesn't defect in the show, which is an unforgivable error) character in HBO's Rome. Our manuscripts can't actually decide on what Pullo's name is. Our manuscripts say stuff like Pulfio, Puleio, Pulio, etc.--Pullo is only a conjecture, and not necessarily the most widely-accepted. Pullo's name is hard to determine in part because no other individual with that cognomen is known to have existed, in any of the forms that our manuscripts have--in most other cases the issue is that several people with similar names could make sense in context, but we don't actually know which one (for example, was Clodius' scriba for his tribunate named Cloelius or Clodius?). Another area where corruptions can cause problems is in the case of magistracies. Sometimes magistracies were swapped for each other in our manuscripts, occasionally causing problems where people that we know held a certain magistracy are listed as having a different one for that year in certain manuscripts. That's actually a relatively rare problem and it's usually easy to solve, although there's a good example that I've been dealing with recently. In 62 Caesar was accused by a guy named Novius Niger of having been involved with the Catilinarians. He only appears in Suetonius (unless the Lucius Novius that Asconius mentions as Clodius' colleague in the tribunate of 58 is the same person), and the text appears to be possibly corrupt. Our manuscripts of Suetonius say that he was a quaestor, but that seems improbable. Suetonius describes Novius as naming several of the supposed accomplices in what appears to be some sort of investigation, and it seems unlikely that a quaestor would be in charge of such a thing, since the quaestor...well, had nothing to do with such duties. Most editors conjecture that the reading should be not quaestorem but instead quaesitorem, making Novius a quaesitor, a special judge appointed to head the investigation and eventually the trial of Catiline's accomplices.