Absolutely critical disadvantages. Here's some more that annoyed me and still do since I am forced to use it at work.
I use my phone a lot to clip pages, add to lists, set reminders on my notes. The clipper on iOS is horrible, takes little pictures of the webpages which you can't actually copy and paste text from later. It also only lets you clip to notebooks you have open on the device.
Plus, if you forget to open the ON after you clip, it will not be synced to your other devices or windows application
There is no way to set reminders (or outlook tasks in Onenote) unless you are using the Desktop application. Not even in the UWP application that is supposed to replace the desktop app.
The recent notes section only shows notes from that device. It's a different list of notes on every device you open it on. There's also no history on the new UWP like in the desktop app.
You can not sort by date, or see the date on a note was created in the preview view. You have to open the note to see the date...unless you accidentally remove it, then it's just gone .
If you draw over text, drop an image in a document, it looks great. If you look at the same document on a phone, the drawing is moved somewhere else. Be careful not to make changes that will get saved, or your desktop will look the same.
If you have a lot of notes, your phone app will be huge because it downloads the notebooks when you open a note. My onenote app was over 15 gb at one point and the only way to stop it is to close notebooks.
That being said, there are advantages:
it is free. Most people can also get some freebies to expand the maximum size from 5 to 15 or even 30gb.
it is great to use with excel documents because you can just update the excel sheets right in the note. Works great with all office apps, and sharepoint.
You can share notebooks, notes with other users without having to worry if they are premium users who can't see a note over 20mb.
There's version control. You can go back to a previous version of the document (This is what causes a lot of the sync issues)
If you are a student, they are really pushing the education aspect. You can follow classes, fill out quizes, do math formulas...