First of all, congratulations, Bjorn for the Tiled 1.0 release. It's really great to see all these workflow improvements.
I do have a bug report regarding the custom properties panel and how mouse click render the Edit and Rename icons below inactive. As a summary of the observation of the bug: the Edit/Rename buttons are inactive until a custom property a mouse click has been registered AFTER a custom property has been previously selected. It looks like a delayed state situation, where you're one mouse click too late for querying the selection state.
To reproduce the bug in full follow these steps:
-Create 1x custom property in a Layer, or Object (it doesn't matter)
-Upon creation the Edit and Rename buttons are active.
-Deselect the Layer/Object or select another Layer/Object to 'refresh' the panel.
-Select your Layer/Object with the custom property you've just created.
-Note Edit/Rename buttons are inactive.
-Select the custom property. Note Edit/Rename buttons are still inactive.
-Then select any other non-custom property (even the panel headings like 'Custom Properties'). Note Edit/Rename buttons become active.
-Then click on the custom property again. Note that the Edit/Rename buttons become inactive.
This seems to be a bug 1.0 because I'm pretty sure this didn't happen in 0.18.3.