It is not slang, and not a mistake. It is a very widespread non-standard grammatical form, associated most commonly with relatively uneducated working-class people. You will hear this type of usage in various parts of the UK as well. When I saw the title of this post, I actually assumed it was a Cockney character speaking this way, which should indicate how widespread the usage is. Don't make the mistake of thinking that the standard English you learn as non-natives is some pure, correct, version of English. There are all sorts of non-standard grammatical items in different dialects that help make English so interesting. Think of the 'youse' of the Irish, the 'it were fantastic' of Yorkshire, or the 'I already done it' of the Cockney. Having said of all which, students of English should certainly not try and speak like this, even in jest. I hear this as dialect because the speaker is clearly a native speaker, with an accent and a manner of speaking that mark the non-standard usage as being part of a local dialect of some sort. If you speak like this as a student, people will hear what you say as being wrong, period. Observe, remember, but do not repeat.

I don't think its entirely unique to "uneducated" people. At university in the midlands (central England) there were plenty of people who spoke like this and were perfectly intelligent and educated. It's just how certain groups of people speak. When I went to university I spoke with a very "correct" RP accent, and after 4 years there I had picked up a lot of "incorrect" colloquialisms, as well as a degree! I'm certainly not uneducated, and I'm also aware of when what I'm saying is wrong (just as much as these people who say it wrong will most likely say it correctly in a job interview), it's just easier and quicker to say it like that. It's very important that English students learn what these "incorrect" uses mean and it's their choice to use them or not. Also I'm pretty sure there's a tonne of "educated" native English speakers making mistakes every day!

It is uneducated speech. Uneducated speakers substitute "don't" for "doesn't," possibly because it's easier to say. Professional criminals often get started in their careers before graduating from high school, and educated speech is not important in their work, so criminals are often shown as using uneducated speech. In this particular case, "tommy-gun" is 1930s slang, and it sounds like the sort of thing you hear in 1930s movies. I don't know Home Alone II but I think someone is "talking like an old movie." Perhaps this is being done to create a sense of distance, to give a feeling of comedy and play-acting so that we do not feel too frightened by the criminals in the movie.

"Okay I Believe You, But My Tommy Gun Doesn't" would be technically the right way to say this in English. As it's stated by someone who is a gangster, you wouldn't expect a gangster to use the most proper words.

The gun toter is displaying his low position in society by using poor English.