So what steps should George Harrison have taken to prevent himself from accidentally sampling "He's So Fine" in his own song "My Sweet Lord"?
That's an excellent question. The short answer is that "subconscious copying" is bullshit and Harrison should have won that case.
It's worthwhile to note that this wasn't a sampling case per se, it was copying of the composition (subconsciously, no less), not the sound recording**. Harrison was accused of taking the melody for "My Sweet Lord" from some back recess of his mind where "He's So Fine" was still echoing, unbeknownst to him. I've listened to the songs, and yeah they're similar. Not so similar that I would find infringement absent evidence of actual copying i.e. knowledge, intent, bad faith, etc.
<rant>
Being a musician myself, I can confidently tell you that with music, there is nothing new under the sun. There is a finite number of note combinations ("chords"), a finite number of chord progressions with a reasonable number of steps (say, 6 or less), and, while both are objectively large sets, only a small subset of both would sound pleasing to the human ear. That set is further reduced by tonal equivalence--you get about the same mileage out of Am and Am7, or Cmaj in 1st or 3rd position.
Pretty much any ordering of chords that you could classify as "commercially viable" has been played, many times, in many different styles, by many people. While ultimately the combination of melody (notes) + harmony (chords) + tempo + arrangement + timbre/tone + lyrics is infinitely variable, it is remarkably hard to write a song that is truly original in chords and melody and sounds decent to human beings.
Music, like science, is a whole lot of standing on the shoulders of your predecessors. And what your predecessors have done is exactly what people in your culture are tuned to like. Unless an artist is bursting with uncommonly rare musical genius, the "new" songs she writes are going to be made entirely from the DNA of the music that came before her. There are only so many ways of doing D - C - G - D, but there are thousands of songs based on just that. Should Lynyrd Skynyrd get to sue them all because, hey, Sweet Home Alabama?
So I think it's shitty to charge George Harrison with copying The Chiffons, especially since he didn't know he was doing it (independent creation is a defense to infringement). Yes, RHCP's "Dani California" sounds like Tom Petty's "Last Dance", and yes Lady Gaga's "Born This Way" sounds like Madonna's "Express Yourself"--but pretty much every other song we've ever heard is, like, spooky close to some prior song if we look hard enough.
</rant>
**I'm not sure how anyone could ever "subconsciously" insert the actual audio from another song into their own, so sampling is always a conscious choice to appropriate another's music. This may be one reason why some courts treat sampling with such disdain compared to (logically equivalent) copying of compositions.
[B]ecause this case does not involve the isolated recording of a personal telephone call by an out-of-state individual in a nonbusiness setting, or the recording of a phone call by an out-of-state business that has a reasonable, individualized basis for believing that a particular caller is engaged in criminal or wrongful conduct, we have no occasion to determine how the comparative impairment analysis would apply in those or other comparable settings.
A successful [software] tool is one that was used to do something undreamed of by its author. -- S. C. Johnson