Compare with..

[jutfrank]

Unfortunately, the SAT and the GMAT are designed by native speakers and do feature those technicalities.
Here are some examples:

https://www.youtube.com/watch?v=zlUrXH6DhTg

https://www.youtube.com/watch?v=c5iBJOWiC_M

https://www.youtube.com/watch?v=VAZrlNzJgqk

I'm sorry but I just don't agree. Nothing that the people in those videos says has convinced me at all.

I have zero experience of preparing students for the GMAT exam. In fact, I'd hardly even heard of it before this thread, but looking at this website, I found the following outline of what the exam aims to test.

The GMAT™ Exam Has Four Sections:

1. Analytical Writing Assessment—measures your ability to think critically and to communicate your ideas
2. Integrated Reasoning—measures your ability to analyze data and evaluate information presented in multiple formats
3. Quantitative Reasoning—measures your ability to analyze data and draw conclusions using reasoning skills
4. Verbal Reasoning—measures your ability to read and understand written material, to evaluate arguments and to correct written material to conform to standard written English

This is completely as I would have expected. Nothing here makes me think that by using a sentence such as While watching a baseball game, a ball or bat could fly at you at any time, so keep your head up, you are likely to compromise your chances of getting accepted at college. That cannot be true. There are so many other more important things to worry about than trivial pedantry such as this. That's the point I'm making. I'm sorry—I don't really want to argue this point further.

 

[raymondaliasapollyon]

You might want to read that web page further because it says the verbal reasoning section includes the following:

Reading Comprehension, Critical Reasoning, Sentence Correction

 

[jutfrank]

Okay, fine.

 

[Phaedrus]

Passing the building, the vandalism became visible. (Who was passing the building? Pedestrians, obviously. But "passing the building" is still considered a dangling modifier.)

My natural assumption there, considering the sentence without context (is this a dangling modifier?), is that it was the speaker who passed the building.

Further context could override that, of course -- e.g.: Passing the building, the vandalism became visible to them.

Among participial phrases commonly used at the beginning of a sentence, "growing up" often dangles, yet I almost invariably notice it only on reflection.

If you search the COCA corpus with the search terms {. growing up ,}, you will find a plethora of danglers. Here are several:

"Growing up, his parents had never seemed terribly unhappy."
"Growing up, the only time it was hard to talk to her mother was at the supermarket."
"Growing up, the concept of global annihilation wasn't just science fiction."
"Growing up, trees were often my babysitters."

In fairness, I should note that many of the COCA results do not feature danglers.

 

[raymondaliasapollyon]

That corpus finding is not too surprising because dangling modifiers are common enough.
That said, I find educated American people more sensitive to danglers and other technical or prescriptive errors than their British counterparts. A comparison between British learner's dictionaries like the Longman Dictionary of Contemporary English and Merriam-Webster's Advanced Learner's English Dictionary will bear out the claim.

I am wondering whether that difference might have to do with the British education system, which does not emphasizes the teaching of grammar.

 

[Phaedrus]

Quirk et al. (1985) note: "The attachment rule does not apply, or at least is relaxed, in certain cases" (p. 1122). One example they give is of style disjuncts like "putting it mildly" ("Putting it mildly, you have caused us some inconvenience" [ibid.]). I'd probably use "to put it mildly" instead, but the same non-problem, which Quirk et al. themselves are even saying is not a problem for these types of expressions, would technically arise.

You just used the abbreviated absolute construction "That said," which often alternates with "Having said that." Long ago, I argued that "Having said that" dangles when it isn't followed by its implied subject, which is usually "I." The person with whom I was having the debate insisted that it wasn't, and I have come to agree with him. In any case, the above passage from Quirk et al. can be used to defend, e.g., "Having said that, this is the way things are."

Later on, Quirk et al. say that "still less objectionable" are phrases in which "the implied subject is an indefinite pronoun or prop it" -- e.g., "When dining in the restaurant, a jacket and tie are required. ['When one dines . . .']" (ibid.). Lastly, they say that "in formal scientific writing, the construction has become institutionalized where the implied subject is to be identified with the I, we, and you of the writers(s) or reader(s)" (p. 1123). Their examples:

When treating patients with language retardation and deviation of language development, the therapy consists, in part, of discussions of the patient's problems with parents and teachers, with subsequent language teaching carried out by them.

To check on the reliability of the first experiment, the experiment was replicated with a second set of subjects.

-- A Comprehensive Grammar of the English Language, section 15.59. Quirk, Greenbaum, Leech, and Svartvik. Longman, 1985.

It would be interesting to see whether the tests you mention penalize students for such exempted non-errors.

 

[raymondaliasapollyon]

"To put it mildly" is a non-problem, just as "Assuming that ...," "Considering that ..., " and "Generally speaking" are. Such expressions are, I think, so fossilized that the test designers would not consider them incorrect.

And yes, scientific literature contains dangling infinitive phrases used with passive main clauses. The Little, Brown Handbook offers a sentence with the same structure, albeit in a different genre:

To understand the causes, vandalism has been extensively investigated.

But the authors aren't satisfied with it and recast it as follows:

To understand the causes, researchers have extensively investigated vandalism.

In Woe Is I: The Grammarphobe’s Guide to Better English in Plain English, the author notes the following:

"Owners’ manuals, you’ll notice, are chock-full of dangling infinitives. Does this sound familiar?
To activate widget A, doohickey B is inserted into slot C. If the one trying to activate the silly thing is you, make you the subject. To activate widget A, you insert doohickey B into slot C. Or you can delete the you, since it’s understood to be the subject. To activate widget A, insert doohickey B into slot C."

Even within the scientific community, dangling modifiers are not always accepted. The ACS Style Guide_ Effective Communication of Scientific Information (2006, An American Chemical Society Publication) notes the following:

"incorrect
After combining the reactants, the reaction mixture was stirred at room temperature for 3 h.
correct
After the reactants were combined, the reaction mixture was stirred at room temperature for 3 h."