One I've noticed is patterns of misuse of pronoun case in conjoined noun phrases. Americans are more likely to use "me" for the subject, as in "Tom and me did thus and so". The British are more likely to use "I" as the object of a preposition, as in "He gave it to Tom and I". I suspect this is because British teachers are more likely to correct and shame students who commit the first error, so they decide the subject forms are the safer bet.
I was taught a very simple rule around this, if you remove the other person you're referring to, is the sentence still grammatically correct?
So for your example:
> He gave it to Tom and I.
Change it to:
> He gave it to I.
That's clearly weird, so it should actually be:
> He gave it to me.
And then re-incorporating the other person:
> He gave it to Tom and me.
When I see your version in my mind it's a mistake and my theory is it's a common misunderstanding of the rule, consider the following slightly different scenario which is a super common mistake in my experience:
> Me and Tom went to the movies.
That is clearly wrong when applying the rule and should be:
> I and Tom went to the movies.
Although I feel that this sounds better:
> Tom and I went to the movies.
I think that what often happens (at least it did for me) is that children making the above mistake only ever see the correction without being reminded of or taught the actual rule, so they incorrectly assume the rule is something like:
> Always use "I" when talking about yourself and someone else.
I live in South Africa and we use British English, but I would expect the rule to be the same for American English too.
The rule is the same in british and american english. What parent was pointing out is that the type of error that brits vs americans make is different. Which is interesting.
I absolutely hate it when people wrongly say 'I', really makes me cringe. (I don't say anything of course, and hope I don't show it!)
It annoys me so much more than the converse, wrongly saying 'me', because - as you allude to - it sounds like conscious effort, like they thought they were actively getting it right. That may not be true of course, it's just how it comes across to me.
English has largely lost the nominative/accusative distinction with the relative/interrogative pronouns "who" and "whom." The first person personal "I" and "me" are probably next. The nom./acc. distinction doesn't provide any useful information that isn't already conveyed by word order or prepositions. At this point, the distinction is a vestige of earlier forms of the language that were less analytic. And given that even decently educated native speakers fail to make this distinction, it's hard to make the case it's an actual error outside the register of formal writing.