To repro:

1. Open project attached
or
Create a new one, create a prefab from e.g. Cube and add several Cubes from this prefab to scene.
2. Select Cube.
3. Enter the Playmode.
4. Change Scale (e.g. x = 2).
5. Press Apply in Inspector (error in Console appears).
6. Exit Playmode.

Actual result: Scale and other non-Transform options changes are appliable only after exiting the Playmode.
Error in console:
InvalidOperationException: This cannot be used during play mode.
UnityEditor.SceneManagement.EditorSceneManager.MarkSceneDirty (Scene scene) (at /Users/builduser/buildslave/unity/build/artifacts/generated/common/editor/EditorSceneManagerBindings.gen.cs:147)
UnityEditor.GameObjectInspector.DoPrefabButtons (PrefabType prefabType, UnityEngine.GameObject go) (at /Users/builduser/buildslave/unity/build/Editor/Mono/Inspector/GameObjectInspector.cs:355)
UnityEditor.GameObjectInspector.DrawInspector () (at /Users/builduser/buildslave/unity/build/Editor/Mono/Inspector/GameObjectInspector.cs:234)
UnityEditor.GameObjectInspector.OnHeaderGUI () (at /Users/builduser/buildslave/unity/build/Editor/Mono/Inspector/GameObjectInspector.cs:143)
UnityEditor.Editor.DrawHeader () (at /Users/builduser/buildslave/unity/build/Editor/Mono/Inspector/Editor.cs:355)
UnityEditor.InspectorWindow.DrawEditor (UnityEditor.Editor editor, Int32 editorIndex, Boolean rebuildOptimizedGUIBlock, System.Boolean& showImportedObjectBarNext, UnityEngine.Rect& importedObjectBarRect) (at /Users/builduser/buildslave/unity/build/Editor/Mono/Inspector/InspectorWindow.cs:1114)
UnityEditor.InspectorWindow.DrawEditors (UnityEditor.Editor[] editors) (at /Users/builduser/buildslave/unity/build/Editor/Mono/Inspector/InspectorWindow.cs:1028)
UnityEditor.InspectorWindow.OnGUI () (at /Users/builduser/buildslave/unity/build/Editor/Mono/Inspector/InspectorWindow.cs:353)
System.Reflection.MonoMethod.Invoke (System.Object obj, BindingFlags invokeAttr, System.Reflection.Binder binder, System.Object[] parameters, System.Globalization.CultureInfo culture) (at /Users/builduser/buildslave/mono/build/mcs/class/corlib/System.Reflection/MonoMethod.cs:222)

Expected result: Changes are applied to prefab and its instances with no error.

Versions info:
There is no ability to apply changes to prefab in 5.3.6p5 (28930307ad49).
Reproducible in 5.4.1p3 (1b587b7935dc) and 5.5.0b7 (bd91e53964bc)