You're having them in the wrong place ... they should be on the Plot, not the LineSeries.
Try this:
<oxy:Plot Grid.Column="0" Name="Plot" Title="Errors" MouseDown="Plot_MouseDown"
MouseDoubleClick="Plot_MouseDown"
TouchEnter="LineSeries_TouchDown"
MouseDown="Plot_MouseDown"
>
<oxy:Plot.Axes>
<oxy:LinearAxis Position="Left" MajorGridlineStyle="Solid" MinorGridlineStyle="Dash" />
<oxy:DateTimeAxis Position="Bottom" MajorGridlineStyle="Solid" MinorGridlineStyle="Dash" />
</oxy:Plot.Axes>
<oxy:LineSeries ItemsSource="{Binding ErrorsByMinute}" DataFieldX="DateTime" DataFieldY="Value" MarkerType="Circle" MarkerFill="#336699" MarkerSize="4" Color="#336699" />
</oxy:Plot>