This guy had an
unusual Di2 shifting problem. Every gear was hard shifting, the indexing was all the way to one end, and he couldn't reach the biggest cog! It turned out that the hanger was too thick. He had it milled down and then it worked. (see the last few posts in this thread).
But I don't think it ever worked correctly from day one, from the factory. Strange that the bike company didn't test it?
His post 16 says: "after a firmware update is etube, my lbs said they performed some trim adjustment via stubs that is more precise or not available to perform via the shifters. These two things allowed them to trim enough to produce acceptable shifting." I've never heard of e-tube only adjustments, different from the junction box micro-adjustments.
Troubleshooting
Your shifting was working correctly in the past for all your gears?
Once it's finally in those bad gears, does it make noise from chain rub there?
Put it in the big ring, shift to larger cogs, then downshift to the bad cog. Does the chain rub? I use a dollar bill as a feeler to see if there's a slight gap between the chain and the next larger cog. Turn the crank a little and check a few more times. I also look at the chain while turning the crank very slowly on the bike stand, looking for tooth interference with the next smallest cog--the chain link gets pushed slightly then rebounds. This is quite unlikely if the inboard spacing is correct.
If your mechanic used the Park Tool
hanger alignment tool, then the old hanger shouldn't be the problem. Did he have to use the tool to bend it a lot to get it back to alignment? If so, it's not a bad idea to put on a new one, for the small possibility of the old one cracking eventually.
I tipped over my bike this year. it was still shifting okay. So I checked the alignment when I needed a new chain -- and it was very slightly bent. l straightened it with the tool. Shifting seemed fine before or after.
Bad shifting in just in two gears. That's very odd.
I think that a new chain shifts slightly better--a little faster. But it doesn't cause bad shifts with an old chain. Off the bike, I can bend the old chain "sideways" much farther than the new chain, which has less flex there. So that could help with a bit better shifts on a new chain.
Worn cassette cogs
I was thinking about how this would affect shifting. The usual symptoms is a spontaneous gear change when sprinting or standing up. "popping" to a new gear or a loud noise. The chain rides up toward the tips of the badly worn gears.
Do you have the chain trying to jump to another cog at times?
Cassette spacers
On Shimano, all the spacers are the same thickness. A missing spacer wouldn't work at all--two cogs would be jammed together. I suppose the lockring could be loose? but the mechanic would have noticed, I hope.
My older bike had Campagnolo 10 speed, and one spacer was thinner than the others!