Hal Galper is a brilliant teacher. This vid is worth watching more than once.
A method I use to internalize a song is first learn it well enough that it can be played effortlessly in the best sounding positions. Then by ear and in time to play it in different positions other than just the easiest or best sounding ones. If that's really difficult I might stop and slow it down but the point is to quit thinking and just make it happen. Then I learn it that way in at least two unrelated keys.
Having confidence in my time goes a long way towards making fewer mistakes and turning the ones I do make into something less disastrous. I’d highly recommend the Time Guru metronome app that randomly silences whatever percentage of clicks you choose. My time was already good but this app is taking internalization of time to a deeper, more solid unconscious level.