I had the same issue, and I could solve it!
I have about 500 Notes in quite a lot of Folders an Sub-Folders, initially I thought this might be the problem.
The problem occured on my iPhone and my iPad after upgrading to iOS 11.
I never had problems with Notes on my MacBook and iMac.
What I tried, and it didn’t help:
I happened to upgrade to an iPhone X, and then decided to set it up as a new phone - I wanted to be cautious, the main reason beeing these problems with Apple Notes. But the Problem occured also on the iPhone X...
All Updates to iOS 11 (I’m on 11.2.5) failed to solve the problem.
I switched iCloud for Notes of, deleted all Notes from the devices - on both simultaneously, restarted them, opened the clean Notes App, switched iCloud for Notes back on - Problem back.
I also restored my iPad Pro as new - did not help.
What solved the problem - and I never thought it would, because I meanwhile got an new Phone, restored my iPad...:
1st: delete the Notes app, confirm that the contents will be deleted but stay on iCloud.
2nd: turn the device off, switch it back on
3rd: reinstall Notes from the App Store
4th: switch iCloud for Notes back on in Settings (it gets deactivated by deleting the app in the first place)
5th: start the clean Notes App, everything gets downloaded from iCloud.
NOTES APP RUNS SMOOTH!!!!!!
(Fingers crossed, knocking on wood...)
Dear Apple:
I love your products, Apps and services. I can see you hab a hard time lately.
But this problem is widely spread, and as I can see in my family: it’s not connected to having a lot of notes either...
How can it be possible that you didn’t come up with a solution?
And if there is no solution: why didn't you come up with a work around like this one? At least somewhere here in the Forum, that we can find it when googling our problem...
This is VERY disappointing.
Next up:
Spelling correction on iOS completely NUTS. Random capitalization, weird auto correct for very common words...
PLEASE!