diff --git a/cpp/src/arrow/dataset/expression.cc b/cpp/src/arrow/dataset/expression.cc
index e7acac3600b88..16f706ed1a46d 100644
--- a/cpp/src/arrow/dataset/expression.cc
+++ b/cpp/src/arrow/dataset/expression.cc
@@ -681,7 +681,7 @@ Result<Expression> FoldConstants(Expression expr) {
         if (std::all_of(call->arguments.begin(), call->arguments.end(),
                         [](const Expression& argument) { return argument.literal(); })) {
           // all arguments are literal; we can evaluate this subexpression *now*
-          static const Datum ignored_input;
+          static const Datum ignored_input = Datum{};
           ARROW_ASSIGN_OR_RAISE(Datum constant,
                                 ExecuteScalarExpression(expr, ignored_input));
 
diff --git a/cpp/src/arrow/util/future.h b/cpp/src/arrow/util/future.h
index 60ce71cd153d0..2fc040c2e2fa5 100644
--- a/cpp/src/arrow/util/future.h
+++ b/cpp/src/arrow/util/future.h
@@ -54,7 +54,7 @@ struct is_future<Future<T>> : std::true_type {};
 template <typename Signature>
 using result_of_t = typename std::result_of<Signature>::type;
 
-constexpr struct ContinueFuture {
+struct ContinueFuture {
   template <typename Return>
   struct ForReturnImpl;
 
@@ -99,7 +99,7 @@ constexpr struct ContinueFuture {
 
     signal_to_complete_next.AddCallback(MarkNextFinished{std::move(next)});
   }
-} Continue;
+};
 
 template <>
 struct ContinueFuture::ForReturnImpl<void> {
@@ -438,13 +438,14 @@ class ARROW_MUST_USE_TYPE Future {
 
     struct Callback {
       void operator()(const Result<T>& result) && {
+        detail::ContinueFuture continue_future;
         if (ARROW_PREDICT_TRUE(result.ok())) {
           // move on_failure to a(n immediately destroyed) temporary to free its resources
           ARROW_UNUSED(OnFailure(std::move(on_failure)));
-          detail::Continue(std::move(next), std::move(on_success), result.ValueOrDie());
+          continue_future(std::move(next), std::move(on_success), result.ValueOrDie());
         } else {
           ARROW_UNUSED(OnSuccess(std::move(on_success)));
-          detail::Continue(std::move(next), std::move(on_failure), result.status());
+          continue_future(std::move(next), std::move(on_failure), result.status());
         }
       }
 
diff --git a/cpp/src/arrow/util/thread_pool.h b/cpp/src/arrow/util/thread_pool.h
index fb326f4ec21e7..3b611435d06dd 100644
--- a/cpp/src/arrow/util/thread_pool.h
+++ b/cpp/src/arrow/util/thread_pool.h
@@ -95,8 +95,8 @@ class ARROW_EXPORT Executor {
   Result<FutureType> Submit(TaskHints hints, Function&& func, Args&&... args) {
     auto future = FutureType::Make();
 
-    auto task = std::bind(::arrow::detail::Continue, future, std::forward<Function>(func),
-                          std::forward<Args>(args)...);
+    auto task = std::bind(::arrow::detail::ContinueFuture{}, future,
+                          std::forward<Function>(func), std::forward<Args>(args)...);
     ARROW_RETURN_NOT_OK(SpawnReal(hints, std::move(task)));
 
     return future;