I’m sorry, but I have to throw in a slightly different opinion 
I think it has pretty much been established amongst the modern generation of “technical players” out there that the old idea of starting slow and incrementing speed in tiny steps simply does not work!
Think about it; you don’t learn to run by walking a tiny bit faster and faster every day… at some point you have to really switch to “running mode”, which is an entirely different body mechanic than walking. It’s the same with playing fast on guitar… and it is a very common reason for hitting speed plateaus on something! Trust me, I did the same thing hundreds of times in the past. At some point you simply cannot play something any faster, using your “playing slow and accurate” technique, which is where you start when you focus on learning the actual notes in a lick. You have to allow your brain and fingers to switch into a different mode…
There are of course other tips relevant to know about, and it is of course not productive either to start at a target speed that you aren’t even close to being able to play.
Let’s say I want to learn a solo, played a 120bmp - this is how I personally go around learning it.
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First step is to learn the right notes. This means encoding the left hand to play the right notes in the right order. And this is where I agree with the rule about “mistakes stick”… so in this phase I would indeed play very slowly and focus on never making mistakes. On the other hand, during this step I also don’t expect to play the entire thing in time. There might be pauses and such between the individual phrases. The important part is that my left hand knows which notes to play in which order.
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Then I want to play the entire thing, in time with the music. I need to find a speed that is fast enough that I’m sure I’ll use the same technique as I will in the end result - so slower than original recording, but it needs to be fast enough that I’m in “play fast mode”.
For me this is typically anywhere between 70% and 85% of original tempo. If you cannot play the solo at that speed, then I believe you’re trying to learn something that is still too complicated for you. -
Then I need to get it all up to 100%. There are a bunch of sub-tips for this. The most useful are (briefly)
- “Chunking”; Don’t think of each individual note, group them together in 4-8 note patterns that will be programmed into your brain as “one thing”, both with regards to fingering and rhythm. Yes, this is possible… most of our own “signature licks” has been encoded into us like this, we just fire them off without thinking (more than; I want to play that lick now).
- “Speed bursts”; Practice small segments at full speed, then perhaps drop down in tempo a little. Or, if practicing along to a recording, set up a loop and focus on only playing that small segment at speed
- Go beyond the target speed; Another crazy sounding tip that really works… say that you feel 120bpm is simply too much, you just cannot do it. Try setting the tempo to 130bpm, and do your very best to try to play along. You will probably fail, and it will be messy. But when you then drop back to 120bpm it will suddenly feel slow to you, and often that can be what allows you to play it comfortably at that speed. Sounds crazy, I know, but it works and I’ve used it often…
There are much more to say on this topic, but I think I’ve droned on for long enough and probably lost most of you along the way