I have a context menu and checkbox inside it, but checkbox displays not correctly.
<toolkit:ContextMenuService.ContextMenu>
<toolkit:ContextMenu >
<toolkit:MenuItem Click="iLikeIt" Tag="{Binding ElementName=chbox}" Header="{Binding isLikeMe, Converter={StaticResource LikeIt}}"/>
<toolkit:MenuItem>
<toolkit:MenuItem.Header>
<CheckBox Name="chbox" Tag="{Binding}" BorderThickness="1" Content="Рассказать друзьям" >
</CheckBox>
</toolkit:MenuItem.Header>
</toolkit:MenuItem>
</toolkit:ContextMenu>
</toolkit:ContextMenuService.ContextMenu>

As this is a UI issue and not a functional one this is very likely a styling issue with the CheckBox. You will need to apply a custom style to the CheckBox in the ContextMenu so that it looks OK in the inverted colours of the ContextMenu.
Make sure you make it work in both Dark and Light theme though.