Steps to reproduce:

1. Open attached project
2. Open scene "Test"
3. Make sure pivot mode is set to center
4. In hieararchy, multi-select "Cube" and "GameObject" GOs
5. Start duplicating them (ctrl + d) and notice that center point changes between different object pairs

Note: Reselecting objects doesn't make pivot point to return to correct position - shifted pivot point position would persist until editor is restarted. However, if editor is restarted and pivot point is fixed for one object pair other might get messed up instead.

Reproduced with: 2017.2.0a2, 2017.2.0f3, 2018.1.0a2
Not reproducible: 2017.1.2p2