Blender Version
Broken: 2.81, 2.82 (16206b66a2594c286aaf2ce3983f946f1d3d39d3)
Worked: N/A

Short description of error
After duplicating an object in the viewport, outliner will highlight the duplicate as active, but leave blue background on the original

Exact steps for others to reproduce the error

1. Load default scene
2. Select the Cube
3. Note that in outliner, Cube is highlighted (both text and blue background)
4. Duplicate the Cube
5. Note that in outliner, Cube.001 is now highlighted as active (text), but the blue background remains on the original Cube

Thus, Cube is not selected in 3D view, but is in the outliner. E.g. shift-clicking on Camera in the outliner will select both cubes and the camera.