If she was sensible, she’d order a background check on him.

This is just not correct English. I’m not saying it’s not typical of colloquial English, but it is both grammatically and semantically indefensible. (Am I shouting?)

Peter, too, noticed that something was wrong with your example, although, unfortunately, his suggested reformulations introduced new problems, not the least of which was the omission of the necessary comma after the if-clause.

There are numerous ways of reformulating the example to avoid the use of the subjunctive, but all those that I have considered seem strained and somehow unnatural. (The replacement of “she’d order” with “she must have ordered” seems the least objectionable option, but even that is less than satisfactory.)

So, why avoid the subjunctive here, when it is clearly the best tool for the job?

Well, the simple answer is that many of us in the English-speaking world (and not least in England) have forgotten how and when to use it (and even, in many cases, how to recognize it). Moreover, the subjunctive mood often has, to our modern ears, a quaint, old-fashioned sound (particularly when it takes the form of the infinitive without to):

Take pity on the helpless, be they man or beast;

Should he fail to arrive, I shall take a taxi;

Would that I were a younger man….

It is hardly surprising that problems arise with the subjunctive, as it shares its forms with other verb-forms – for example:

If he studied hard, he would pass the exam.

This is barely recognizable as the subjunctive mood, yet a slight reformulation swiftly removes any possible doubt:

If he were to study hard, he would pass the exam.

(I won’t go into the niceties of would and should. Modern English, as you probably know, often uses “would” where “should” would once have been preferred, but that’s a discussion for another time and place.)

Turning to the example that “shows an intermingling of indicative and subjunctive to achieve nuances of meaning”, I sincerely hope that David Crystal had no such idea in mind when citing it. There are no “nuances of meaning” to be gleaned here. The first speaker, A, begins with a statement that is clearly ungrammatical, as it employs the indicative where the subjunctive is required. Nevertheless, B understands A’s intended meaning, and responds appropriately, subtly correcting A as he does so. A then responds with the correct use of the subjunctive, very probably having taken note of B’s correction.

(Alas, A’s second statement, as quoted, introduces another small but significant error – one that I rather doubt David Crystal would have made. Technically speaking, “Well” should be followed by a stop, such as a comma or semi-colon.)

Misusing the indicative for the subjunctive will generally go unnoticed in many circles, and we could probably agree that many worse linguistic crimes often go unpunished. I am thinking, in particular, of such crass catachreses as “if you was” and “if we was”, which, outside the pages of Oliver Twist or Pygmalion, are an offence to any but the least-educated ear.