At the point that you begin to make errors, you have drop the speed to level of having no errors.
If your requirement is to make no errors, then you have to simplify.
You can do that through dropping the speed.
You can simplify many other ways as well. You can go HS, you can skeletonize, you can chunk, you can drop notes, you can loop, etc.
One thing I do frequently is to play a difficult passage at tempo, but reducing it to a small piece, or reducing the changes of notes.
For example. Here's a piece from the brass players world. Sorry about that, I know this is a piano forum, but... we're all musicians here. It's not a virtuoso solo piece, it's simply a difficult piece from the standard band repertoire. http://www.youtube.com/watch?v=oIgjAY55k1g
Rolling Thunder is a classic circus tempo march, normally played at 160. It's a bit demanding for us trombone players - while I don't expect to ever make a mistake sightreading a Sousa march, this is a different challenge that took considerable effort to play at tempo. The trumpet player is pressing a valve down half an inch, I'm moving a heavy slide a couple of feet.
Playing this one at 80 and incrementing a beat at a time, or steps of 5 or 10 will never get you to tempo. Sorry, I've seen people work for years and not get there. I just had a conversation with a good musician who's worked on lip trills out of Arban with the incremental method for 40 years, and didn't succeed.
Well, there's a caveat here too, I guess. Take an highly skilled trombone player skilled at the genre and let him incrementally speed up, he'll get there with the stepwise motion. The other 98% of trombone players will never play this one.
When I worked this one up, I set the metronome to 160, final tempo. I played the first pattern, but on the first two notes. Hard to explain, and so easy to show! There are 13 notes in the first run. I played the first two notes, but continued to play the second note at tempo for the next 11 notes as if I were moving. C-F-F-F-F-F-F-F-F-F-F-F-F Then the first 3 notes in rhythm, and repeated the 3rd note on the rhythm of the next 10. Etc. Master four measures at a time - but sometimes I had to master two notes at a time.
Doing this shows immediately where the difficulty lies. The transition between some notes is easy and others near impossible - and can usually be fixed with a correct fingering choice and a lot of practice.
What I'm saying is yes, you have to simplify; but don't fall into the trap of thinking slowing down is the only way to simplify.
It can be the worst way to simplify.
Once the correct motions at speed are understood, slowing down is often the best way to get real control. But as a first step, particularly for a beginner, it can be very limiting.
I have other objections but they are more philosophical so I'll spare you.