With the following example content, clicking at the end of the line selects the image and triggers a clickOn. This prevents me from for example creating a new empty paragraph below the existing one by using the mouse and pressing Enter.

I would suggest not triggering a clickOn event and simply putting the cursor behind the inline node. This seems to be a regression as I did not have this problem with earlier versions of ProseMirror (e.g. 0.7.0).
I'm not seeing this problem on the master branch. If I have an image node as the last node in a textblock, clicking after it consistently puts the cursor after it.
I'm sorry I tested this with 0.8.3 and you are right that this works fine on the master branch :) Great!
Fixed in master again.
I can confirm this is now working for image nodes :)
But I just found another case where the clickOn gets triggered when clicking at the end of the line. I have a Paragraph containing a single inline node, which is rendered with the following DOM structure:

(In this case I want to handle the clickOn event when the node is clicked to overwrite the default href click behavior.)
I just noticed that this issue is closed, but I am still experiencing the problem I described in my last comment with inline nodes that are not images. Would be really great to have a fix or a workaround for this as I have multiple nodes using the described DOM structure. I assume that the incorrect selection and clickOn behavior is caused by the same issue.
Yeah, I still had the email starred to look into it, but I'll reopen the issue as well.
Patches 0d2968494 and 806d13fff031a make this go away even for nodes with children.