So, the sequence of actions that leads to the broken map editor functionality:
There is a polygonal layer.
1) I select the "Edit geometry" tool and select any polygon on the layer - vertices are highlighted.
2) Do nothing, just select "Box selection" tool and select features from the layer
3) Press "Delete" button - the dialog is shown, let's choose "Clear" button.
Now only one feature is deleted from the selection and seems everything is broken because of this deadlock...
Commands stop to work, try zoom for example after this...