diff --git a/ci/minimum_versions.py b/ci/minimum_versions.py
index cc115789d0f..08808d002d9 100644
--- a/ci/minimum_versions.py
+++ b/ci/minimum_versions.py
@@ -20,6 +20,12 @@
 
 channels = ["conda-forge"]
 platforms = ["noarch", "linux-64"]
+# these packages don't fail the CI, but will be printed in the report
+ignore_failure_packages = [
+    # remove when we can pin to pydap 3.5.1 without error
+    "pydap",
+]
+# these packages are completely ignored
 ignored_packages = [
     "coveralls",
     "pip",
@@ -171,7 +177,11 @@ def compare_versions(environments, policy_versions):
     status = {}
     for env, specs in environments.items():
         env_status = any(
-            spec.version > policy_versions[spec.name].version for spec in specs
+            (
+                (spec.version > policy_versions[spec.name].version)
+                and (spec.name not in ignore_failure_packages)
+            )
+            for spec in specs
         )
         status[env] = env_status
     return status
diff --git a/ci/requirements/min-all-deps.yml b/ci/requirements/min-all-deps.yml
index fc55280a17b..03e14773d53 100644
--- a/ci/requirements/min-all-deps.yml
+++ b/ci/requirements/min-all-deps.yml
@@ -42,7 +42,7 @@ dependencies:
   - pandas=2.1
   - pint=0.22
   - pip
-  - pydap=3.5.0
+  - pydap=3.5
   - pytest
   - pytest-cov
   - pytest-env
diff --git a/pyproject.toml b/pyproject.toml
index 5494d4ab484..8fb1975c232 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -346,6 +346,8 @@ filterwarnings = [
   "default:the `pandas.MultiIndex` object:FutureWarning:xarray.tests.test_variable",
   "default:Using a non-tuple sequence for multidimensional indexing is deprecated:FutureWarning",
   "default:Duplicate dimension names present:UserWarning:xarray.namedarray.core",
+  # Zarr 2 V3 implementation
+  "ignore:Zarr-Python is not in alignment with the final V3 specification",
   # TODO: this is raised for vlen-utf8, consolidated metadata, U1 dtype
   "ignore:is currently not part .* the Zarr version 3 specification.",
   # TODO: remove once we know how to deal with a changed signature in protocols
diff --git a/xarray/tests/test_backends.py b/xarray/tests/test_backends.py
index e37f73c8004..1d9c90b37b1 100644
--- a/xarray/tests/test_backends.py
+++ b/xarray/tests/test_backends.py
@@ -2320,6 +2320,9 @@ def roundtrip(
             with self.open(store_target, **open_kwargs) as ds:
                 yield ds
 
+    def test_roundtrip_bytes_with_fill_value(self):
+        pytest.xfail("Broken by Zarr 3.0.7")
+
     @pytest.mark.parametrize("consolidated", [False, True, None])
     def test_roundtrip_consolidated(self, consolidated) -> None:
         expected = create_test_data()
@@ -3548,6 +3551,10 @@ def test_append(self) -> None:
                 )
 
     @requires_dask
+    @pytest.mark.skipif(
+        sys.version_info.major == 3 and sys.version_info.minor < 11,
+        reason="zarr too old",
+    )
     def test_region_write(self) -> None:
         ds = Dataset({"foo": ("x", [1, 2, 3])}, coords={"x": [1, 2, 3]}).chunk()
         with self.create_zarr_target() as store:
diff --git a/xarray/tests/test_dataarray.py b/xarray/tests/test_dataarray.py
index febf89cc0ab..8d0d5011026 100644
--- a/xarray/tests/test_dataarray.py
+++ b/xarray/tests/test_dataarray.py
@@ -3608,8 +3608,8 @@ def test_to_and_from_dict(
         return_data = array.to_numpy()
         coords_data = np.array(["a", "b"])
         if data == "list" or data is True:
-            return_data = return_data.tolist()  # type:ignore[assignment]
-            coords_data = coords_data.tolist()  # type:ignore[assignment]
+            return_data = return_data.tolist()
+            coords_data = coords_data.tolist()
 
         expected: dict[str, Any] = {
             "name": "foo",
diff --git a/xarray/tests/test_duck_array_wrapping.py b/xarray/tests/test_duck_array_wrapping.py
index 59928dce370..42440385928 100644
--- a/xarray/tests/test_duck_array_wrapping.py
+++ b/xarray/tests/test_duck_array_wrapping.py
@@ -101,6 +101,14 @@
     },
 }
 
+try:
+    import jax
+
+    # enable double-precision
+    jax.config.update("jax_enable_x64", True)
+except ImportError:
+    pass
+
 
 class _BaseTest:
     def setup_for_test(self, request, namespace):
diff --git a/xarray/tests/test_variable.py b/xarray/tests/test_variable.py
index 388f51bc568..8569cb093e7 100644
--- a/xarray/tests/test_variable.py
+++ b/xarray/tests/test_variable.py
@@ -2444,7 +2444,8 @@ def test_to_index(self):
 
     def test_to_index_multiindex_level(self):
         midx = pd.MultiIndex.from_product([["a", "b"], [1, 2]], names=("one", "two"))
-        ds = Dataset(coords={"x": midx})
+        with pytest.warns(FutureWarning):
+            ds = Dataset(coords={"x": midx})
         assert ds.one.variable.to_index().equals(midx.get_level_values("one"))
 
     def test_multiindex_default_level_names(self):