diff --git a/xarray/core/variable.py b/xarray/core/variable.py
index d6ef206e7b5..52bcb2c161c 100644
--- a/xarray/core/variable.py
+++ b/xarray/core/variable.py
@@ -2084,19 +2084,33 @@ def rolling_window(
             var = self
 
         if utils.is_scalar(dim):
-            for arg in [window, window_dim, center]:
-                assert utils.is_scalar(arg)
+            for name, arg in zip(
+                ["window", "window_dim", "center"], [window, window_dim, center]
+            ):
+                if not utils.is_scalar(arg):
+                    raise ValueError(
+                        f"Expected {name}={arg!r} to be a scalar like 'dim'."
+                    )
             dim = [dim]
-            window = [window]
-            window_dim = [window_dim]
-            center = [center]
-        else:
-            if len(dim) != len(window):
-                raise ValueError(
-                    "'dim', 'window', 'window_dim', and 'center' must be the same length. "
-                    f"Received dim={dim!r}, window={window!r}, window_dim={window_dim!r},"
-                    f" and center={center!r}."
-                )
+
+        # dim is now a list
+        nroll = len(dim)
+        if utils.is_scalar(window):
+            window = [window] * nroll
+        if utils.is_scalar(window_dim):
+            window_dim = [window_dim] * nroll
+        if utils.is_scalar(center):
+            center = [center] * nroll
+        if (
+            len(dim) != len(window)
+            or len(dim) != len(window_dim)
+            or len(dim) != len(center)
+        ):
+            raise ValueError(
+                "'dim', 'window', 'window_dim', and 'center' must be the same length. "
+                f"Received dim={dim!r}, window={window!r}, window_dim={window_dim!r},"
+                f" and center={center!r}."
+            )
 
         pads = {}
         for d, win, cent in zip(dim, window, center):
diff --git a/xarray/tests/test_variable.py b/xarray/tests/test_variable.py
index fa07714bba6..1aaaff9b2d4 100644
--- a/xarray/tests/test_variable.py
+++ b/xarray/tests/test_variable.py
@@ -948,6 +948,27 @@ def test_nd_rolling(self, center, dims):
             )
         assert_equal(actual, expected)
 
+    @pytest.mark.parametrize(
+        ("dim, window, window_dim, center"),
+        [
+            ("x", [3, 3], "x_w", True),
+            ("x", 3, ("x_w", "x_w"), True),
+            ("x", 3, "x_w", [True, True]),
+        ],
+    )
+    def test_rolling_window_errors(self, dim, window, window_dim, center):
+        x = self.cls(
+            ("x", "y", "z"),
+            np.arange(7 * 6 * 8).reshape(7, 6, 8).astype(float),
+        )
+        with pytest.raises(ValueError):
+            x.rolling_window(
+                dim=dim,
+                window=window,
+                window_dim=window_dim,
+                center=center,
+            )
+
 
 class TestVariable(VariableSubclassobjects):
     cls = staticmethod(Variable)
@@ -2198,23 +2219,23 @@ def test_datetime64(self):
 
     # These tests make use of multi-dimensional variables, which are not valid
     # IndexVariable objects:
-    @pytest.mark.xfail
+    @pytest.mark.skip
     def test_getitem_error(self):
         super().test_getitem_error()
 
-    @pytest.mark.xfail
+    @pytest.mark.skip
     def test_getitem_advanced(self):
         super().test_getitem_advanced()
 
-    @pytest.mark.xfail
+    @pytest.mark.skip
     def test_getitem_fancy(self):
         super().test_getitem_fancy()
 
-    @pytest.mark.xfail
+    @pytest.mark.skip
     def test_getitem_uint(self):
         super().test_getitem_fancy()
 
-    @pytest.mark.xfail
+    @pytest.mark.skip
     @pytest.mark.parametrize(
         "mode",
         [
@@ -2233,24 +2254,27 @@ def test_getitem_uint(self):
     def test_pad(self, mode, xr_arg, np_arg):
         super().test_pad(mode, xr_arg, np_arg)
 
-    @pytest.mark.xfail
-    @pytest.mark.parametrize("xr_arg, np_arg", _PAD_XR_NP_ARGS)
+    @pytest.mark.skip
     def test_pad_constant_values(self, xr_arg, np_arg):
         super().test_pad_constant_values(xr_arg, np_arg)
 
-    @pytest.mark.xfail
+    @pytest.mark.skip
     def test_rolling_window(self):
         super().test_rolling_window()
 
-    @pytest.mark.xfail
+    @pytest.mark.skip
     def test_rolling_1d(self):
         super().test_rolling_1d()
 
-    @pytest.mark.xfail
+    @pytest.mark.skip
     def test_nd_rolling(self):
         super().test_nd_rolling()
 
-    @pytest.mark.xfail
+    @pytest.mark.skip
+    def test_rolling_window_errors(self):
+        super().test_rolling_window_errors()
+
+    @pytest.mark.skip
     def test_coarsen_2d(self):
         super().test_coarsen_2d()