I observed this issue when testing my scene in the editor's player. I was also able to reproduce it in a test scene that only contained the InputField.

At first, the caret was not visible at all. By changing the pivot of the "InputField Input Caret" child game object to (0, 0), I was able to get the caret visible, although offset to the left and down. I tried adjusting the pivot (in the editor), and also the rect transform's anchoredPosition (in script) slowly to bring the caret back towards the input field, but as soon as the caret would intersect the input field, it stopped rendering. This makes it so that I can never get the caret inside the actual text input field's bounds. I also tried changing the z value of the input caret to see if I could get it to draw on top of the input field, but this did not help either.

Me too. On OSX no caret in input field.

On OS X I don't see the caret at all.

I see all the same issues as described in http://issuetracker.unity3d.com/issues/caret-does-not-appear-in-the-input-field-and-cannot-select-the-text