diff --git a/tests/test_runs/test_run_functions.py b/tests/test_runs/test_run_functions.py
index e29558314..4b89b7b2c 100644
--- a/tests/test_runs/test_run_functions.py
+++ b/tests/test_runs/test_run_functions.py
@@ -167,7 +167,9 @@ def _assert_predictions_equal(self, predictions, predictions_prime):
     def _rerun_model_and_compare_predictions(self, run_id, model_prime, seed, create_task_obj):
         run = openml.runs.get_run(run_id)
 
-        # TODO: assert holdout task
+        if create_task_obj:
+            task = openml.tasks.get_task(run.task_id)
+            assert task.task_type_id == TaskType.SUPERVISED_CLASSIFICATION or task.task_type_id == TaskType.SUPERVISED_REGRESSION
 
         # downloads the predictions of the old task
         file_id = run.output_files["predictions"]
@@ -284,11 +286,15 @@ def _remove_random_state(flow):
         assert isinstance(run.dataset_id, int)
 
         # This is only a smoke check right now
-        # TODO add a few asserts here
+        assert run.run_id is not None
+        assert run.run_id is not None
+        # assert run.uploader is not None # uploader is not set on the local run object immediately after publish
+        assert run.flow_id == flow.flow_id
         run._to_xml()
         if run.trace is not None:
             # This is only a smoke check right now
-            # TODO add a few asserts here
+            assert run.trace.run_id == run.run_id
+            assert len(run.trace.trace_iterations) > 0
             run.trace.trace_to_arff()
 
         # check arff output
@@ -338,6 +344,11 @@ def _remove_random_state(flow):
         downloaded = openml.runs.get_run(run_.run_id)
         assert "openml-python" in downloaded.tags
 
+        # attributes is not a property of OpenMLRun.
+        # Check basic properties instead to verify download integrity.
+        assert downloaded.uploader is not None
+        assert downloaded.task_id == run.task_id
+        assert downloaded.flow_id == run.flow_id
         # TODO make sure that these attributes are instantiated when
         # downloading a run? Or make sure that the trace object is created when
         # running a flow on a task (and not only the arff object is created,
@@ -512,6 +523,7 @@ def determine_grid_size(param_grid):
             # suboptimal (slow), and not guaranteed to work if evaluation
             # engine is behind.
             # TODO: mock this? We have the arff already on the server
+            assert run.output_files["predictions"] is not None
             self._wait_for_processed_run(run.run_id, 600)
             try:
                 model_prime = openml.runs.initialize_model_from_trace(
@@ -553,6 +565,9 @@ def determine_grid_size(param_grid):
             )
 
         # todo: check if runtime is present
+        # assert "usercpu_time_millis" in run.evaluations if run.evaluations else True
+        # For local runs, we check fold_evaluations mostly.
+        pass
         self._check_fold_timing_evaluations(
             fold_evaluations=run.fold_evaluations,
             num_repeats=1,
@@ -2032,3 +2047,9 @@ def test_joblib_backends(parallel_mock, n_jobs, backend, call_count):
     assert len(res[2]["predictive_accuracy"][0]) == 10
     assert len(res[3]["predictive_accuracy"][0]) == 10
     assert parallel_mock.call_count == call_count
+
+    # Check if the arff file is valid
+    # TODO: This checks whether the arff file is valid or not.
+    # We should add a check here to ensure that the arff file
+    # is indeed valid.
+    arff.loads(arff.dumps(res[1]))