So, I've made a mini experiment. Some important things before I tell you exactly what and what. This is my first technic set....the biggest and most complex one...my other lego sets are 2nd generation bionicle....and skyline architecture sets...so small sets...what I wanted to experiment is to see for myself how these gears work and since I don't have lego motors to hook up and see the pistons moving like probably most of you guys did....I had to appeal at this old fashion...which yeah probably it isn't that accurate but....better than nothing:
https://www.flickr.com/photos/188882501@N03/shares/Y63LYH
So what I did exactly:
1) I built the first box, but with the minimal changes that I could do from the errata without using new pieces (I didn't want to unbuild my bionicle), meaning that I replaced the pin in step 5, I used @Attika's solution and lastly I switched step 267 with 269 (gear sequence fix) and I tested the car and indeed it still had a lot of friction especially in gears 3 and 4, meaning that I needed to do the entire errata build if I wanted to see a difference
2) I though to myself (let's try the stock version, it couldn't be that bad) so I rebuilt the first box exactly as in the instructions and...just hear me out please:
The gearbox works perfectly....I have no friction at all...and the speeds actually work correctly. The pistons don't move right...that's true but the gear speeds are in the right order. That's what I found out with my slingh shot experiment. I put a duct tape line so I would pull the sling shot equally everytime...when the pistons move the slowest, aka how the 4th gear should be in reality but in this lego technic this is the 1st gear....the car went the furthest....almost hit the wall.....then in the second gear...when the pistons move 2nd faster (aka 3rd gear on pistons speed), the car travelled significantly less distance then the first gear, moving to the 3rd gear, the car travelled again less then the second gear...but no significantly, and again in the 4th gear when the pistons move the fastest...the car travelled the least amount of distance...tho it was very close to the 3rd gear.....I've redone the test 3 times....and everytime....it worked perfectly....1st gear = the farthest, 2nd gear = close to 1st, 3rd gear = close to 2nd, 4th gear = close to 3rd. I pushed the car in the band, I pulled the band and just put the car in front of it, I have tried different variations of "sling shooting" the car, and each time it worked normally. (I have locked the front wheels so it would go straight forward)
Now I know you people might say that...this doesn't prove anything, that this isn't math which I've seen you've already done with the gear ratios, but...it's a practical test, that for me at least (unless I'm dumb and got the conclusion wrong in which case I would like you people to point it out to me), proved that the gearbox works how it should work (besides the reverse 4 gear part you know). I mean, yeah the pistons are wrong....but you guys, testing the gearbox by looking at the pistons (I'm assuming this because I dunno how else you figured it out that the gearbox is flawed) tells me that the problem is with the pistons alone and not the gearbox. I mean if I build the full car...the pistons aren't visible anymore...and I switch gears...I happens what it should....car's wheels turn easily, than a little bit harder and harder with each speed I switch, which is in fact what it is supposed to do.
I know that probably the errata fixes the pistons and keeps the gearbox intact and has less friction and so on, but for someone who doesn't have technical parts to spare and also don't wanna buy other pieces, I think the gearbox works just perfect. If anything, you guys have some spare time and are bored, try this testing method, see how the vehicle works not how the pistons move, and see for yourself (again tell me if I'm wrong) that the stock version of the gearbox does what it's supposed to do...I mean...with the sequence....the reverse and the 1-4 4-1 jumps are not normal but hei....it's a toy after all.
Another test could be to build some sort of ramp, let the vehicle go from the same height and see how far it goes. I've done this one because that's what I had around at home but I assume that the ramp test would actually be more accurate.