The difference between these two forms are often so subtle!!!!

If I accidentally use one case instead of the other, will people still understand what I'm saying? Or can somebody give me examples of mixing up the two cases would result in expressing a different message?

Thanks

You should try to learn the difference between at least Nom. and Gen. every time you learn a new noun. It's a critical part of the language. Accidents happen, especially when learning a language, but my experience is that, if native speakers hear you make a mistake like this, unless you're undergoing some course of language study with them, they will generally switch to English to make it easier for both parties to communicate. You might get away with it at conversation groups intended for language learners, but the standard of the language at these types of events will generally be lower, and you shouldn't be hoping to "get away with it" anyhow. Best thing to do is aim not to make the mistake, and make a point of learning the forms when you're learning your vocab.

Alright. I just wish that the system for genitives and plurals was more systematic. I have heard that there is some lee-way with switching one plural suffix for another.

I will indeed make it a point to study both cases of each noun that I learn. However, I will say that the fact that some nouns have the same form for both cases makes me think that communication will not be hindered; that is to say, there wont be another thing that I'm accidentally saying.

Is it correct to say that I won't accidentally be saying something else by mixing up the two cases?

The system for case in Irish is actually fairly regular, at least in the modern language. If you're interested in learning that system, you're going to have to crack into the grammar books and learn about declensions. The declensions categorise nouns based on how their forms differ when declined, and if you're not familiar with the declensions, the system may seem arbitrary to you. The book you're using, Teach Yourself Irish isn't the best for this. After introducing only the first and second declensions, and discussing them primarily in the context of prepositions (p. 35-36), it kind of glosses over the rest, only giving a single paragraph on the third, fourth and fifth declensions (p. 66). It doesn't really give a proper description of the declensions; what they are, how they work, why they're important; and it provides no examples for declensions 3-5 until the appendix (p. 193-196).

I wouldn't pay too much attention to the fact that some nouns (specifically nouns of the 4th declension) are the same in the Nom. and Gen. singular. That doesn't mean it's ok to treat nouns of all declensions that way. For example, in English, just because the plural for fish is also fish, or the plural for sheep is also sheep, that doesn't mean that fluent speakers wouldn't notice quickly if you just used the singular form for all nouns in English. Granted, English speakers are generally very used to speaking language learners for whom English might be only a second or third language. They get a lot of practice interacting with such learners, and generally can't just switch to another language the learner speaks more fluently. That's not the case for Irish, and for a lot of other minority languages, where speakers will often just switch to whatever the local majority language is if they think it will make communication easier. So if you want people to speak with you in Irish, you're probably going to have to get yourself to a higher proficiency in the language than you would if you were learning a language like English.

Generally speaking, you might not be saying something else if you mix up the cases, but you won't be saying what you intend to either. Mostly, it'll just sound strange to speakers, though they may even have trouble understanding what you're trying to say. It'd be akin, maybe, to mixing up syntax in English where it marks the genitive, like if you said "I'll see you in the yard school" instead of "school yard", or "I'm going to the hall city" instead of "City Hall". There are situations when you will be saying something else entirely, though. For example, if you use the first or second declension Nom. singular instead of a Gen. singular, you will actually be using the Gen. plural, because the forms are the same. Best to just avoid making the error.