So, no. Don't allow yourself to make mistakes. Take the challenging section, come up with a drill for just that section, and work that section until it is perfect at the same tempo where you can play the rest of the piece. The first rule of time-efficient practice is to spend your time on the sections that need perfecting! Just playing the piece through over-and-over is not a good use of practice time.
Another thing that I found a bit mind-bending, given my own music education, is that our teacher had the philosophy that first you memorize the piece, and only after the piece is completely memorized without intonation and tempo mistakes, is it possible to start really working on perfecting it. That is the point where she really started teaching the piece. Maybe that is a violinist thing where there is a culture of memorization, but it was a bit of a new concept for me.
Another teacher at a violin camp used to say: "After you first succeed, try, try again." Meaning, don't stop after you get it right! After you get it right, you need to play it correctly at least as many times as you played it incorrectly, just to reach net-zero learning. Only then can you play it correctly many more times in order to perfect it.
> Don't allow yourself to make mistakes. Take the challenging section, come up with a drill for just that section, and work that section until it is perfect at the same tempo where you can play the rest of the piece.
Work that section until it is perfect implies that when you start it's not perfect, i.e. mistakes are made. You can't just be perfect with everything all of the time. How would you even know where to start such as to "make no mistakes"? Finding perfection is the process I tried to describe above, you aim to play perfectly and get as close as possible. Nevertheless, errors are inevitable. Embrace their necessity for they are the stuff of learning.
> One drill is to play that scale run forwards and backwards, slowly, concentrating on perfect intonation, even timing, and percussive finger landings.
Reiterating, doing 50 reps of the above is bound to have some errors. You notice them, your brain notices them. If you only ever played things that you can currently do perfectly, or said differently, vacant of any mistakes, how would you ever get better or play new things which are bound to have things you can't already perfectly do?
I think what I failed to portray is that yes, don't "allow yourself to make mistakes." Care about trying to be perfect. You'll still make mistakes and that's a good thing. As you constantly improve and take on more and more challenging tasks, you're also baking in countless reps that are strengthening the "right" networks in the brain and pruning out the ones that aren't right.
I recommend checking out the podcast because I'm definitely not doing a good job of replicating his lessons / sharing of what the latest in neuroscientific literature shows.
I don't know what your background is with musical instruments, but there is a mental wall to break through when it comes to how "acceptable" errors should be.
If you practice and make mistakes, you are building up muscle memories for the wrong notes.
As a piano player, what OP says wrings very true. It's tempting to just "play the piece" to practice it, but this is very inneficient, for the reason stated above. focused repetitions is order of magnitudes faster.
Granted I'm not a pianist, but a jazz bassist. So I see it in light of the technical problems of the bass, which include intonation and tone formation. My approach is, if I'm struggling with a passage, I don't just keep playing it over and over. Rather, I stop and try to analyze what's hard about it, and what I'm doing wrong with my technique. Then I work on correcting those problems.
This is also what my kids' teachers do during lessons. Part of the reason for lessons is to learn a better approach to practicing.
A lot depends on what kind of music you're playing, but I often don't know what I'll be playing until I find out at the performance. The bassist is often the one who's expected to roll with whatever the rest of the band chooses. So the mastery of specific pieces can't just be an end unto itself, but it also has to pay off in improving my ability to approach the next piece. This requires making real progress on technique.
My poster child example of this is tracking falling down when ice skating / skiing.
Not falling is a poor metric of success as you see many people not fall but are also clearly not ice skating. Falling is to some extent a metric of how hard you are pushing yourself.
With instruments, practising mistakes can be costly because establishing muscle memory is habit formation and baking in mistakes is essentially inefficient in your time spent learning.
As my teacher would say "practise like you are up on the stage in front of thousands. Perform like you are alone at home in your pyjamas."
Don't be afraid to make mistakes, but always practise smart. (FWIW I spent the best part of 15+ years NOT practising smart)
This is at odds with a quote from OP's second point:
> If you keep making mistakes when practicing then you are just going to get good at making them, so it’s best to avoid them in the first place.
That aside, the article seems like great advice. With Huberman's account of encouraging adult neuroplasticity in mind, my thinking would be to amend this method towards going just fast enough to be able to do the chunk of music but not so slow that the attempts are free of errors. And probably the errors should be of one type at a time? Instead of erring in dynamics and fingering and articulation all at once, try to get everything right except for one aspect. For that, attempt to surpass your abilities and err.
[0] https://www.youtube.com/c/AndrewHubermanLab/featured
Edit: Said another way, “perfect practice makes perfect,” where you aim to play perfectly but consistently just barely fall short. The correct networks are strengthened while those tiny errors get tweaked via neuroplasticity the nights after and consistent improvement results.