How to handle objections to the wording of test questions or answers? I try to include a wide range of difficulty in the questions on quizzes and tests, from very obvious to quite subtle. The more subtle questions might hinge on a distinction of singular vs plural or other 'wording' aspects, so that those who have the strongest grasp of the material can differentiate themselves. I usually get a good spread of numerical grades, so experience says that I am doing this correctly.

But students who missed an item based on subtleties often speak up when I review the quiz or test immediately after all the results are in. It would seem impolitic for me to say that I made that item difficult deliberately, but it is true. Instead I usually point back to the textbook or my lecture to say that I actually explained and even stressed the point. Sometimes I agree that wording was poor in a question and so I give everyone credit (essentially acting as if the question did not exist). This can vary from year to year.

In a workplace subtleties will be vital, so it is not a manufactured situation to include them in my teaching, and I only use subtle distinctions in tests where they exist in the material, and are worth emphasizing.

How do you handle situations where students push back on the wording of test questions or answers? How do you not simply say, "Because that way I have a more useful test"?
I am not sure what you mean by a "useful test" in this context.  If your goal is to create a bell curve with English speakers at the top, you could administer the verbal section of the SATs. 

You say that your students are complaining because what you actually wanted from them was unclear without an eagle-eye reading (and from your own accounts, it sounds like this is the case).  If this is the case, then their complaints are legitimate.  It is perfectly reasonable for them to be upset that you are trying to trip them up in a manner orthogonal to what they are actually studying. 

I'd like to differentiate two different forms of testing.  The first is meant to enhance pedagogy by plumbing the depths of a topic.  A great pedagogic test creates an occasion for students to consolidate what they know, but it also provides a means of discovery.  Almost everyone that I have ever spoken to about this can remember testing events when, after reading a question, they suddenly understood something that they had been missing about the topic itself.  This sort of test simply allows students to demonstrate whether or not they understand the material, which forms a sort of philosophical boundary.  If all of the students understand the material, all of the students will achieve close to top marks.

There is another form of test which is designed to rank students.  The boundaries here are different, and there is some psychological brinksmanship involved. Even if all of the students understand the material, they will not all achieve top marks.  There are a number of ways to accomplish this.  One is to simply ask a lot of tiny, very detailed questions.  Another is to use questions about the subject that don't even have to be particularly hard; you simply have to set enough traps.  The best and most capable students fall for the fewest traps (or so the thinking goes). Of course, using this second method causes resentment.

But very fundamentally, the goals and means of these two types of tests that are fundamentally different from each other. By trying to combine them, you ultimately wind up with a test that is good at neither.  And if students expect pedagogical tests that are designed simply to test knowledge, but instead they receive ranking tests, they will feel that their trust has been breached.  When students do not trust their teacher, learning is dampened.

We should not resort to verbal trickery to differentiate between students.  Make the questions harder by forcing them to integrate the material more deeply, or use it at a more advanced level.  They can reasonably become confused about how to accomplish the difficult task you have set before them.  They should never become confused about what that task is in the first place.