Hello! I'm having the same problem, but with a few different parameters.
yEd version 126.96.36.199, Java version 1.8.0_74, running on windows 7.
For me, there is no correlation to the "Finger" icon as anon mentioned.
This feels like it might be two separate problems.
The first problem is that, when I select an element, it takes about half a second to populate the Neighborhood and Properties windows. That wouldn't be a problem, except that F2 (Edit Label) is entirely ignored until they populate.
The second problem is basically as described above: Sometimes pressing F2 causes the text box to appear, but without highlighting the contents or making the cursor appear. After this happens, the arrow keys cause the selection to move to another element, rather than moving the cursor within the text box.
I notice a peculiar behavior *most* of the time when this happens. The text box becomes momentarily highlighted, then goes back to its un-highlighted white color. (This makes me suspect a race condition, or maybe a late input event is screwing things up.)
I'd be happy to test this further. This program is fantastic, and this bug is slowing me down bigtime. Thanks.