diff --git a/seaborn/_core/plot.py b/seaborn/_core/plot.py
index 2abd64e79e..2c735a9287 100644
--- a/seaborn/_core/plot.py
+++ b/seaborn/_core/plot.py
@@ -1263,12 +1263,16 @@ def _setup_split_generator(
                 order = categorical_order(df[var])
             grouping_keys.append(order)
 
-        def split_generator() -> Generator:
+        def split_generator(dropna=True) -> Generator:
 
             for view in subplots:
 
                 axes_df = self._filter_subplot_data(df, view)
 
+                if dropna:
+                    with pd.option_context("mode.use_inf_as_null", True):
+                        axes_df = axes_df.dropna()
+
                 subplot_keys = {}
                 for dim in ["col", "row"]:
                     if view[dim] is not None:
diff --git a/seaborn/_core/properties.py b/seaborn/_core/properties.py
index 68836cd045..95539dc6f4 100644
--- a/seaborn/_core/properties.py
+++ b/seaborn/_core/properties.py
@@ -312,6 +312,7 @@ class ObjectProperty(Property):
     normed = False
 
     # Object representing null data, should appear invisible when drawn by matplotlib
+    # Note that we now drop nulls in Plot._plot_layer and thus may not need this
     null_value: Any = None
 
     def _default_values(self, n: int) -> list:
@@ -720,7 +721,11 @@ def get_mapping(
             raise TypeError(msg)
 
         def mapping(x):
-            return np.take(values, np.asarray(x, np.intp))
+            ixs = np.asarray(x, np.intp)
+            return [
+                values[ix] if np.isfinite(x_i) else False
+                for x_i, ix in zip(x, ixs)
+            ]
 
         return mapping
 
diff --git a/seaborn/_marks/basic.py b/seaborn/_marks/basic.py
index 2d5d8d38a5..a79e99bd96 100644
--- a/seaborn/_marks/basic.py
+++ b/seaborn/_marks/basic.py
@@ -1,6 +1,7 @@
 from __future__ import annotations
 from dataclasses import dataclass
 
+import numpy as np
 import matplotlib as mpl
 
 from seaborn._marks.base import (
@@ -35,13 +36,15 @@ class Line(Mark):
 
     def _plot(self, split_gen, scales, orient):
 
-        for keys, data, ax in split_gen():
+        for keys, data, ax in split_gen(dropna=False):
 
             keys = resolve_properties(self, keys, scales)
 
             if self.sort:
                 # TODO where to dropna?
-                data = data.dropna().sort_values(orient)
+                data = data.sort_values(orient)
+            else:
+                data.loc[data.isna().any(axis=1), ["x", "y"]] = np.nan
 
             line = mpl.lines.Line2D(
                 data["x"].to_numpy(),
diff --git a/seaborn/_marks/scatter.py b/seaborn/_marks/scatter.py
index b5d4a0bcc8..85642ff33e 100644
--- a/seaborn/_marks/scatter.py
+++ b/seaborn/_marks/scatter.py
@@ -67,7 +67,7 @@ def _resolve_properties(self, data, scales):
             filled_marker = [m.is_filled() for m in resolved["marker"]]
 
         resolved["linewidth"] = resolved["stroke"]
-        resolved["fill"] = resolved["fill"] & filled_marker
+        resolved["fill"] = resolved["fill"] * filled_marker
         resolved["size"] = resolved["pointsize"] ** 2
 
         resolved["edgecolor"] = resolve_color(self, data, "", scales)
@@ -91,7 +91,6 @@ def _plot(self, split_gen, scales, orient):
         # (That should be solved upstream by defaulting to "" for unset x/y?)
         # (Be mindful of xmin/xmax, etc!)
 
-        # TODO pass scales *into* split_gen?
         for keys, data, ax in split_gen():
 
             offsets = np.column_stack([data["x"], data["y"]])
diff --git a/seaborn/tests/_marks/test_scatter.py b/seaborn/tests/_marks/test_scatter.py
index e5f0a6b8ca..9f751f95bb 100644
--- a/seaborn/tests/_marks/test_scatter.py
+++ b/seaborn/tests/_marks/test_scatter.py
@@ -1,5 +1,6 @@
 from matplotlib.colors import to_rgba, to_rgba_array
 
+import pytest
 from numpy.testing import assert_array_equal
 
 from seaborn._core.plot import Plot
@@ -139,3 +140,15 @@ def test_filled_unfilled_mix(self):
 
         expected = [mark.edgewidth, mark.stroke]
         assert_array_equal(points.get_linewidths(), expected)
+
+    @pytest.mark.parametrize("prop", ["color", "fill", "marker", "pointsize"])
+    def test_missing_semantic_data(self, prop):
+
+        x = [1, 2, 3]
+        y = [5, 3, 4]
+        z = ["a", float("nan"), "b"]
+
+        p = Plot(x=x, y=y, **{prop: z}).add(Dot()).plot()
+        ax = p._figure.axes[0]
+        points, = ax.collections
+        self.check_offsets(points, [1, 3], [5, 4])