1) Additionally, please ensure that no text or important information appear within 0.25″ of the edges of the cover (0.125″ from the trim line, and 0.125″ of bleed beyond it).
The problem with this sentence is “appear.” When two nouns are joined by “or,” they do not for a plural subject, as they do when they are joined with “and.” If the sentence read “no text and important information” then “appear” would be correct; as it is, the “or” necessitates a singular verb: “no text or important information appears.”
2) Just think, manufacturing and shipping is taken care of.
Same thing, but different. “Manufacturing and shipping” form a plural subject, and so need a plural verb, which, in this case, should be are.
3) The Senior Advocacy Center, which acts as a local voice for seniors and is comprised of about 45 attorneys, doctors, social workers who raise money to help seniors, would like to talk to Sonju but she hasn’t agreed to talk to them, Castro said.
We have an entire post devoted to the “comprise” versus “compose” issue not too long ago. To recap (the short version): you never say “comprised of” because a large thing is composed of small things, while small things comprise a large thing. For example, a jury is composed of jurors, but jurors comprise a jury.
4) Investigators have searched her cell and interviewed neighoring inmates and so far haven’t found evidence that she smoked pot in the jail.
Terrible sentence. Typo with the “neighboring” is the first problem, but then there’s the mess caused by not using commas, plus I hate that insinuating “so far.” Excuse me? Is it just a matter of time before evidence is found? Oh, no. It’s either there or not.
I’d rewrite the entire sentence like this: Investigators have searched her cell and interviewed neighboring inmates, but have found no evidence that she smoked pot in the jail.
5) The group posted a message on their Facebook page , asking for volunteers from across the U.S. to make this reunion happen, wrote ABC News.
“The group” is a collective noun and, therefore, is singular, which means you cannot use a plural pronoun.
Corrected: The group posted a message on its Facebook page , asking for volunteers from across the U.S. to make this reunion happen, wrote ABC News.
6) A law enforcement official, who was not authorized to discuss the details and spoke to The Associated Press on condition of anonymity, said the SUV T-boned the limo.
I have a serious problem with this sentence. Material between commas is known as “parenthetical” information: information is not necessary to the sentence and can be removed completely with no damage to the sentence’s meaning. Well, if you remove the bit about the official “who was not authorized…,” you’d have someone speaking with authority, and that changes the meaning of the sentence completely. The part about the official not being authorized to comment is integral to the meaning of the sentence, so take out those commas.
7) Paul will be designing his gourmet menu from locally-harvested foods.
Never hyphenate an —ly adverb. “Locally harvested” is correct.
8) The meal is preceded by an Art Sale, offered “Fresh off the Easel” by the internationally recognized  “Light Chasers of the Sun Coast”, Plein Air Artists, who will be painting “till the sun goes down” and selling their works, wet and dry, on the Farmhouse lawn throughout the evening.
At a minimum, put that comma after “Coast” inside the quotation marks. I’d also do a pair of dashes around “wet and dry” to set off that concept. Actually, it’s a lousy sentence and needs to be completely rewritten.
9) In case you were wondering, the owner did get their phone back.
“Owner”—singular. One owner. “Their”—plural pronoun. No can do. If you read the sentence, it’s obvious the writer knows the sex of the owner, so “he” or “she” would have been correct.
10) We can’t thank Purebred Breeder’s enough for bringing “Dudley” into our lives.
Yikes! “Breeders” is the plural of “Breeder.” The only time you use an apostrophe to create a plural is with individual letters (the M’s) or an abbreviation with periods in it (M.B.A.’s). Otherwise, it’s “s” or “es.”
11) Your book remains in-stock, without inventory, made on-demand when customers order.
Generally speaking, when a compound adjective follows the noun that it is modifying, you do not hyphenate it.
the in-stock book; the book was in stock
the on-demand book; the book was printed on demand
12) The right argues that a faculty that has teachers and principals who have carry permits and can protect the children under their car is the way to go.
Sloppy, sloppy! It’s not “car,” it’s “care.”
13) Every author wants to sell a million copies of their book, but most won’t sell more than a few thousand.
Write like that and you won’t sell one! “Every author” is singular; “their book” is plural. It has to be “his or her book,” or you could say “All authors want to sell…” and that’d be correct. As it is, BOO!
14) WHAT: Water Moccasins (Cottonmouths) – This venomous snake makes its home in the water. Though considered a shy snake, it’s bite is quite serious and sometimes deadly.
The most common punctuation/grammar mistake rears it’s, I mean its, ugly head! I always double-check my use; its, I mean it’s, such an easy mistake to make! Plus, that hyphen is wrong. I would stick a period after (Cottonmouths).