I can't speak for Mayan texts, but Egyptian being completely wrong is basically impossible. We have such an understanding of Egyptian text and language that we can tell when an Egyptian scribe makes a mistake. There may be elements that are incorrect regarding a particular glyph, but completely wrong is highly improbable. I know when you look at hieroglyphs they look like they couldn't possibly contain any meaning, but they really aren't that bizarre when you've learnt even just the basics. I find Egyptian much easier to translate than languages like Latin, even though that uses the same alphabet as us.

We are so confident we can read them correctly that we can notice things like shifts in the spoken language from say, Old Kingdom to New Kingdom, based on variations in spellings (Loprieno, Ancient Egyptian, a linguistic introduction). We can also track the development of the language over time. A text from around 2600 BCE, like the Pyramid texts, would be easily distinguishable in grammar and vocabulary from one of the New Kingdom in the mid to late 2nd millennium BCE.

Considering the similarities between Coptic, a known language, and Egyptian, plus principles of linguistics regarding consonant shifts, there is too much evidence that we are right. The grammar is consistent with related languages, such as verbal systems in other ancient and modern languages.

Egyptian is partially uniliteral, meaning there are symbols for single consonants. Thus, we can track names that have been passed down through known languages, such as for countries, peoples, or kings. Indeed, this is how Champollion managed to decode it in the first place, by taking the names of Ptolemaic royalty and known Egyptian names and working backwards (Allen - Middle Egyptian).

The existence of texts with both Egyptian and other language versions. Obviously, there is the Rosetta Stone, but there are other extant examples such as the Treaty between Hattusili III of Hatti and Ramesses II, of which there are Akkadian, Hittite and Egyptian language versions (Beckman Hittite Diplomatic Texts, p96; See Breasted AR for the Egyptian version). These versions have slight differences but the fact that they all say basically the exact same thing is proof that three difference languages convey the same meaning.

Another rather interesting little tidbit is the onomatopoeic nature of Egyptian animals, which gives a really good indication of the sounds represented by the symbols conforming to reality. The Egyptian word for cat is mjw, pronounced 'mioo'. Remind you of anything? How about this one, donkey is a3/'3, originally ja3/j'3, pronounced 'ee-a-ah'. My favourite is lion, rw, pronounced 'roo'.

If we had it wrong, there is no way, considering the vast corpus of Egyptian texts, that we could have gotten so far without noticing grammatical and lexical contradictions within these texts.

These are two different situations, but with some theoretical similarity. I'll address the one I know better.

Deciphering a language is like putting together a puzzle. Each syntactical unit, symbol, glyph, etc. is a puzzle piece. Now in a normal puzzle, each piece is connected to ~4 other ones. You have to match up the images, but in the end what matters is that each edge interlocks with its neighbors. If it fits the image and all four edges, it’s the right piece. The difference, though, is that each piece only goes to one spot in one puzzle. A glyph appears in any number of phrases. So instead of fitting the edges of one puzzle, a common glyph needs to fit in 500 puzzles. For every single piece we have to crosscheck 500 different holes, and a different set of 500 holes for each piece. (Yes... this is going somewhere)

Now, Mayan translation is a relatively recent thing. There are plenty of glyphs that we just don't know yet. Egyptian translations are relatively complete. Many Mayan translations right now are filled with question marks, slashes, and “possibly”s. Yet there’s still a large amount of glyphs whose accuracy I’ll fight you on. I've outlined here the various things that make decipherment possible, so I'll go more specifically into the Mayan side of those things:

• There's a lot of Mayan texts: We have stairways and walls and ceramics and giant stone pillars covered in text. It's on jewelry and temples and everything. This is what the "500 puzzles" are all about. If I propose a translation for one symbol, that translation has to work with most every other instance of that symbol. Suppose a bit I'm working on says "He gave the victorious general a celebratory unknown glyph." I see an image of these two characters beneath the text, and one holds an axe, so I fill in "axe" for the blank and move. Moving on with my studies, I come across the same glyph, but typically preceded by the "he ate/drank" glyph. He ate... an axe? Well, somethings gotta change. The piece fit in one puzzle's empty space, but not in the other 499. Each instance of a glyph is another opportunity to double check it and make sure everything makes sense.

• Mayan is still spoken: Or, rather, many languages in the Mayan family are still spoken, and by millions of people at that. Yucatec, K'iche', Ch'ol.... we have the entire linguistic family tree of the language that Mayan hieroglyphs recorded, both its descendants and its cousins. Thus, we have a very good idea of what they should say. We can expect a number of things common to Maya languages: an ergative-absolutive pronoun structure, agglutinating verbs with tense marking prefixes, mediopassive and positional moods, and certain word roots. In the same way, if you knew an undeciphered script recorded a descendant of English, you would look for a strict word order, uninflected nouns, and lots of prepositions and auxiliary verbs. Because of this, we basically have a rough image of what our finished puzzle should look like- we’re not just trying random word combinations to see what fits, we know the structure and sounds of the language.

• Numerical elements are hard to screw up: The majority of Classic Maya texts are historical ones. "On this day, Bird Jaguar IV took the throne." "3 years, 4 months, and 25 days later, he battled the city of Piedras Negras. He captured this and that general." Stuff like that. Thankfully for us, they have very regular structure. Each event and phrase is preceded by a calendrical marking. Now calendars have two parts: numbers and units. Numbers are hard to mess up. There are bars, dots, "moons," and shells. We never see more than 4 dots, so bars must equal five. With just those two symbols, we never see more than 3 bars and 4 dots, so one of the others must be be twenty. We see "moons" with bars and dots, but not shells. Thus shells are zero and "moons" are twenty. What about units? We know a lot about Mayan numbers and calendrics from historical/modern sources, so we're not exactly working from nothing. But our readings of codices show perfect calculations of predicting the phases of Venus and monuments that mention eclipses and the like line up perfectly with documents elsewhere in the world. so we gotta be doing something right. Back to the historical texts. Here's a quick formulaic rundown of how early translation went. I stick with variables to make it clear how the process went without introducing assumptions of meaning prematurely. The numbers and letters represent chunks of glyphs.

Since we know the dates, we essentially have inscriptions that look like this:

In 600 AD, 1 X. In late 623, 2 X. In 674, 3 X.

It appears to be a series of events with repeating elements and a variable one. This repeating element "X" only appears on other monuments in sections that have dates between 600 and 674. Sometimes X will have a number in it, and sometimes on we can find something else, Y, that's exactly the same but with a number one lower. Now on another inscription we see:

In 577, 1 Y. In 598, 2 Y. In 600 X Y 4. In early 623, 3 Y.

What's so special? Well, the numbered glyphs are the same across each inscription, even across different sites, but the lettered ones are different. As for the numbers, "1" is always first, "3" is always last, and every time they set the bounding dates of when we see X or Y. "2" and "4" are usually a similar distance from "1". The only time we see X in the same place as Y happens to be the same date as the first time we ever see X. The "2" of X also is frequently shortly after the "3" of Y. These patterns occur again and again.

Once we see patterns, we start filling in blanks. It's clear that these are series of events, narratives. Certain elements, the numbers, are always the same- these are probably our verbs. That makes the letters our actors. "1" is always first, and the people never appear before that, so it must mean "was born." "3" is always last, usually 50-70 years after the birth, so it must mean their death. People appear in older people's stories with verb "4" on the same day as their birthday, so "4" must mean "gave birth to." When this older person dies, their child's verb "2" follows shortly after. This verb glyph also looks like a hand grabbing a royal scepter or someone sitting in the same manner kings are depicted in Maya art. We’ll thus translate it as “takes the throne.”

Now that’s a very bare bones approach, and I hope it made sense. Once we move on from the easier, very common verbs like siyaj “was born” or ch’am k’awil “to take the scepter,” we encounter all kinds of difficulties. As mentioned before, we’re nowhere near done. But, to get back to your original question, how do we know we’re not wrong? Think back to the puzzle. Or even better, building a Lego set. If you get one thing wrong, nothing works. You can put your brick one stud off, and then come back 50 steps later and find that the whole thing will not fit together. There are simply so many pieces which interlock to create our understanding of Mayan script, many which I’ve barely touched on: syllabic spellings that reinforce translations, colonial records, glyph with clear graphical origins (i.e. ch’ak, “axe,” looks like an axe), spelled out foreign words… Every translation is supported not by just a couple data, but by a whole network of data points with connections going everywhere. Either it’s right, or the whole darn thing is wrong. And what we have works outrageously well as a predecessor to modern Mayan for something that’s completely wrong.