We can take a look at BBC News for an example of a quoted American (source):
"I struggled with it myself for a long time, but I came to realise that life is that gift from God," [Mr Mourdock] said.
Now let's look at the New York Times quoting a Briton (source):
“I think what he’s achieved will never be bettered in terms of five consecutive Games,” Hoy said. “You start to realize what it means when you actually break it down and see what you have to do and the number of things that can go wrong.”
Unfortunately, many style guides overlook your exact question, but we can see in practice what news sources do. Short of poring over hundreds or thousands of articles from each outlet, it's hard to tell if they are all consistent, but generally the publisher or author will use the spelling conventions of the publisher's or author's country unless quoting directly from a text.
How do we deal with other aspects of a dialect or accent (e.g. preserving someone's g-droppin', etc.)? The answer is, as per some style guides such as the MLA Handbook:
Obvious typographic errors may be corrected silently (without comment or sic; see 13.59), unless the passage quoted is from an older work or a manuscript source where idiosyncrasies of spelling are generally preserved. If spelling and punctuation are modernized or altered for clarity, readers must be so informed in a note, in a preface, or elsewhere.
Note that this describes "typographic errors". However, the quoted speech you describe is transcribed at some point. If you choose to preserve someone's speech verbatim, then you will wind up capturing typographic and grammatical "errors". Therefore, you could apply this guideline.
When quoting a speaker, if she said, "I ain't got nofin' to cook wif," then I could use [sic] or an alternative. It's often suggested, as in this ELU question that "quiet editing" take place, so you would write "I have nothing to cook with" or "I ain't got nothing to cook with" depending on how you want to portray the speaker.
In short, go with your gut instinct.
The sentence 'It was good' is grammatically correct, if a little thin-sounding.
Adding the appositive 'the movie' after the sentence (with the standard comma to set off the parenthesis) is still quite acceptable, and sounds more idiomatic.
There is the hint of an afterthought here (because of the 'tagged on' construction), which conveys the impression that real thought has gone into the judgement being expressed. This in turn can convey an impression of a measure of reserve, unlike say with 'Wow! THAT was good!'
Best Answer
This is a construction that is restricted to certain dialects of US English. In Standard English, it is not grammatical. (This construction is also often stigmatized, which means you would want to be especially careful before using it — you could be judged!)
However, this construction is used systematically in certain dialects of American English. To describe it clearly, I want to define a few linguistic terms I will use to sort out a crucial three-way distinction:
People who use this "might could" construction are not making a speech error — within this dialect, it is grammatical. Informally, this is used throughout the southern US, but has not spread to any other region I am aware of. Interestingly, it so happens that the same construction is standard in German.
A description of how this works:
What is going on in "might could" constructions is a process called "modal stacking", where multiple modal verbs (e.g. "could", "should", "might", "would", etc.) can be stacked on top of each other. Each added modal verb contributes towards the overall meaning of the sentence. In Standard English, to convey the same meaning, we have to use another construction:
We are doing effectively the same thing in standard English in terms of semantics, it's just that we have to change things around to get around a syntactic restriction.
These constructions are not redundant by definition (they are only redundant if you stack them redundantly!). Neither "I might do that" nor "I could do that" would have the same meaning as "I might could do that".
Other constructions include:
To sum up:
Modal stacking is not sloppy, meaningless, or redundant; linguistically, it is a systematic process (which I think is really cool!). It is just non-standard in English — something one would avoid using outside of this particular dialect group, especially because (like many features of Southern English) it carries a certain stigma outside of where it is used. But within that group, it is a productive and useful construction.
(This answer has been edited to clarify my use of "grammaticality".)