Just recently (like 10 days ago) Microsoft has deployed some changes to SharePoint Online and specifically to the links to individual documents that you could obtain by just clicking on the context menu. This way of providing a link to someone was very quick and easy, hence heavily used by lots of people. It's just a click, compared to using the Share function or "Get a Link".
The only thing you need to be sure of is that the person that you give the link already has access to this document. Otherwise using the "Get a Link" feature would be more useful. But it also has the disadvantage - you are breaking the permission structure using these links and you don't know where your link will travel after you give it to the person... if it's an anonymous link this can even get out of the boundaries of your organization! Not a good deal of control there...
Few days ago, when I tried to share a document (a project plan in the Microsoft Project .mpp format) in this way - the user got "Page not found" error. Same thing when I tried to open the link :) Both of us have access to that document anyway.
So... I looked up the link and saw that it looks like this:
An interesting fact is, that when I tried the same thing with Word / Excel / PowerPoint documents - all workred like a charm (like in the good old days - 10 days ago :). The links contain the same document ID, but they open fine in the browser.
After some research on the topic and a quick call with MS support, they advised me that this behavior is "by design" - great job Product teams. So from now on, every document that can't be open in Office Online (Office Web Apps) e.g. anything but Word, Excel, PowerPoint would fail and the user has to manually modify the link before providing it to another user - how usable is that?
There's also a Yammer hot thread on this... you can check it out in the next 12 days... before the IT Pro Yammer network becomes history, which is another sad topic and a poor decision in my view.
Of course... meanwhile we could still use the "Get a Link" feature and forget about the good permission practices in the organization. At least I recommend not using the anonymous links, unless you absolutely need this shared with someone outside of the organization.