This question is a lot simpler to answer when considering written material. The truth is, we're a lot more aware of our words when we write them down. We have time to look at them, "listen" to them a few times, think about them, tweak them. And yes, I regularly come upon instances of the obvious (two, to, too; there, their, they're; etc.) but I really can't hit people too hard for those things. Often, they're just typos. It happens to all of us. (Secret: almost every time I write the word "two," I first write "tow," which does not turn up as an error in spellcheck.) We become blind to those errors, especially when the word sounds the way we want it to. Spelling and usage can be real nuisances. So when I answer this question, I'm not going to talk about any of those things. Instead, I'm going to have to say the most common flub I see is...
Was vs. were.
This is complicated and deserving of a post of its own, but basically, if your character is speculating about something that may or may not happen or that he or she wishes will happen, often that character has slipped into what's called the subjunctive mood. When the character is in the subjunctive mood, they *often* need to use the word "were" rather than "was."
Here's a famous example: "If I were a rich man." This character is speculating. He's not rich, but he wishes he were. Therefore, he is in the subjunctive mood, and "were" is the correct linking verb here.
It's often a simple matter of looking at the sentence and figuring out the character's tone before committing to a was or were. If the sentence has the word "if" in it, that is often a sign (see the example above). Sometimes, characters are more obvious: "I wish I were eating." Here, the character is blatantly NOT doing the action, which means he is in the subjunctive mood.
(Side note: there are some people who will tell you that the words "was" and "were" should never be used, or if you must use them, you should do so only very sparingly. These folks believe that the past tense of the verb "to be" automatically equals passive voice, and passive voice is similar to a thinly veiled form of blasphemy. But this is simply not true, and it often leads to impersonal, stilted, or otherwise awkward sentences. Sure, just as you shouldn't overuse any word, try to provide some variance in your verb selection. But if someone tells you not to use "was" or "were" ever because it always means you're writing in the passive voice and the passive voice is bad, just smile and nod and move along. That person will catch on eventually. Passive voice has to do with the relationship of the verb with the subject and object. "To be" does not mean passive voice is happening.)
Question Two: oral grammar
This is a different matter altogether. Verbal language is an area that I, personally, don't feel should be as closely scrutinized. This is because language evolves, and it tends to do so vocally before it does on paper. Plus, if you're simply speaking to a friend, and if that person is from the same place, you are going to use slang, idioms, phrases of speech that are not particularly "correct" but are funny.
For example, I use the word "I'ma" a lot. As in, "I'ma go get a haircut." There are zillions of words that are common vernacular that would drive a grammarian mental. So, that's my disclosure.
The most common grammatical error I hear is the use of the word "is" in a contraction. For example, "There's six books on the shelf." "There's some leftovers in the fridge." "There's twenty or so kids coming to the birthday party."
Here's the rule: if the subject of the sentence is plural, you need "are" rather than "is." "There are six books on the shelf." There are some leftovers in the fridge." "There are twenty or so kids coming to the birthday party."
(I know what you're thinking: who in their right mind would have twenty kids at a birthday party? Sush. This is for example purposes.)
The problem here is that "are" just doesn't lend itself well to contractions. "There're six books on the shelf," is a bit weird. But seriously, are we too lazy to speak the extra word? Eh, maybe. But there you have it.
I hope that answers your question, Darlene.