In this phrase:
Stop picking at that, it’ll just get worse.
Should the comma be replaced by a semicolon, or is the usage of the comma also acceptable?
Yes, it should be a semicolon. What you have are two independent clauses; you can’t just splice them together with a comma.
Disagree, if it’s dialogue. People don’t speak in semicolons. The comma version is much more natural.
huh?
Well, dialogue is a whole different animal, of course. It’s acceptable to bend or break the rules when it serves the flow or style. But in any other case, that’s where you’d need a semicolon. 
In dialogue, a semicolon sounds just like a comma; that is, it may be indicated by a brief pause, but this is not mandatory.
Yes to both halves of your question. A semicolon is preferable but short sentences, particularly in dialogue, are often, and properly, joined with commas. (There’s no real bright line division between what’s permissible and what’s a ‘comma splice’ solecism, but almost any good editor will draw the line between acceptable and not at just about the same point.)
Choie, semicolon-length pauses do occur in normal speech patterns, though typical speech patterns tend to seldom use related-but-distinct clauses in colloquial usage. “I got my first real six-string; bought it at the five-and-dime.” Bryan Adams strikes me as having a good sense of colloquial speech. A period would IMO be too much of a disconnect for how the song’s natural flow joins the clauses, though it certainly would not be incorrect. But the natural sense of how the two song lines flow in speech seems to call for a semicolon.
I was told once by an English professor in college that she could actually hear the semicolons punctuating my sentences when I spoke.
FWIW, a different English professor (who had had exposure to my writing before he actually met me) said, upon our first actual conversation, “I thought your writing was stilted and artificial, but Jesus, you really talk like that.”
So there.
Do you have a cite on that? I’ve never heard anything but a bright-line rule on this topic. In casual writing, such as a letter to a friend, I’d let it slide, but when the OP summons grammar Nazis I think we’re looking for an approach strict enough to please the most rigorous stickler.
The Chicago Manual of Style, 14th ed., § 5.89: “[A semicolon] should always be used between the two parts of a compound sentence (independent, or coordinate, clauses) when they are not connected by a conjunction.”
There’s no leeway there, just an “always.” That’s how I learned 'em; that’s how I write 'em.
That’s awful, but very funny.
You called?
I learned that if you have two independent clauses, then you must use a semicolon. Joining sentences with a comma but not a conjunction is always a comma splice. But if there’s an authority that says otherwise, I’d be most interested in reading what they have to say. A cursory googling didn’t turn up anything.
Gaudere’s Law strikes. I probably should have used something stronger than a comma, such as an em dash.
Drat.
personally i would use a period.
That’s a different version of the statement, though. A period would provide a marked pause, while the comma implies they are almost run together.
As for the comma thing: I wish I had my old English book which said it was okay for certain sentences. One example was “I think, therefore I am” rather than “I think; therefore, I am.”
Aren’t you referring to the rule mentioned most recently by Inner Stickler? Isn’t ‘therefore’ being used as a conjunction?
^ i agree. “therefore” is a conjunction. if a comma is acceptable for joining two independent clauses with no conjunction then you would be able to write “I think, I am.” rather than “I think; I am.”
As per the OP, a comma is wrong imo. A semicolon or even a hyphen would be what you were looking for. I have never heard of different rules governing dialogue.
It’s not called the Chicago Manual of Incontrovertible Rules That Must Apply to Everything in All Situations. This is a matter of style, and is a judgment call. Organizations use style guides to create a consistent quality to writing to help present a single face to readership. Novelists and playwrights aren’t bound by such things. If a comma would most effectively communicate to a reader the style of speech, then a comma is the best way to go.
Tina Blue is hardly an authority, but here she gives a delightfully simple and well-argued explanation of when a comma splice is acceptable, quoting Barbara Wallraff, who is considered something of an authority. (I couldn’t find an online direct cite of Wallraff, as opposed to people like Blue quoting her.)
The Wikipedia article on comma splices likewise quotes Strunk and White and also Fowler as to their acceptability in joining short clauses.
And, as Blue notes, “You wouldn’t have a problem with the comma in this sentence, would you?” I have never seen an editor or copyeditor insist on a semicolon in such usages, but by the absolute rule’s terms “would you” is an independent clause that should require a semicolon to set it off.
How to use a semicolon. Brought to you by the oatmeal. Enjoy 
Wouldn’t a colon work?