The tabs of SlidingPanes are not rendered (sized) properly is the SlidingPane is containing a nested Splitter. The issue is not reproducible with 2014.2.724 version of the controls.

Reproduction code:
        <telerik:RadSplitter ID="RadSplitter2" runat="server" Skin="Metro">
            <telerik:RadPane ID="RadPane1" runat="server" Width="22px">
                <telerik:RadSlidingZone ID="RadSlidingZone1" runat="server" Width="22px">
                    <telerik:RadSlidingPane ID="RadSlidingPane2" Title="What If" runat="server">
                        <telerik:RadSplitter ID="WhatIfPaneSplitter" runat="server" Width="50px">
                            <telerik:RadPane ID="RadPane2" runat="server"></telerik:RadPane>
                            <telerik:RadPane ID="RadPane3" runat="server"></telerik:RadPane>
                        </telerik:RadSplitter>
                    </telerik:RadSlidingPane>
                </telerik:RadSlidingZone>
            </telerik:RadPane>
            <telerik:RadPane ID="RadPane4" runat="server"></telerik:RadPane>
        </telerik:RadSplitter>

Potential workaround is attached but it requires modification of the markup to add a class to the pane that holds the vertical sliding zone as well. If you do not need this fixed urgently, wait for an official fix.

RadSplitter is loaded with the gray background when configured with Default/Silks/Bootstrap skins in RenderMode="Classic".

The issue applies to RadFileExplorer and RadEditor file browser dialogs too which use RadSplitter inside.

The background is white in version 2017.1.118.40 and earlier.

Workaround:
Switch to RenderMode="lightweight"

or 

RadSplitter: Apply the BackColor property to RadSplitter or its RadPane items.
RadFileExplorer: 
ASPX:
<telerik:RadFileExplorer ID="RadFileExplorer1" runat="server" RenderMode="Classic">
    <Configuration ViewPaths="~/"  />
</telerik:RadFileExplorer>
Codebehind:
using Telerik.Web.UI;

public partial class Default2 : System.Web.UI.Page
{
    protected void Page_Load(object sender, EventArgs e)
    {
        (RadFileExplorer1.Splitter.GetPanes()[0] as RadPane).BackColor = System.Drawing.Color.White;
        (RadFileExplorer1.Splitter.GetPanes()[1] as RadPane).BackColor = System.Drawing.Color.White;
    }
}

The text of the tabs inside a SlidingZone is not displayed properly when the SlidingZone is updated via AJAX. 

Steps to reproduce:
Run the following code and click a button inside a SlidingPane.

<telerik:RadSplitter ID="RadSplitter1" runat="server">
<telerik:RadPane ID="RadPane1" Scrolling="Both" Width="30px" runat="server">
<telerik:RadSlidingZone ID="RadSlidingZone1" runat="server" Width="30px">
<telerik:RadSlidingPane ID="RadSlidingPane1" runat="server" Title="Menu 1" Width="280px">
<telerik:RadButton runat="server" ID="btn1" AutoPostBack="true" Text="Update SlidingZone"></telerik:RadButton>
</telerik:RadSlidingPane>
<telerik:RadSlidingPane ID="RadSlidingPane2" runat="server" Title="Side Menu Two" Width="280px">
<telerik:RadButton runat="server" ID="btn2" AutoPostBack="true" Text="Update SlidingZone"></telerik:RadButton>
</telerik:RadSlidingPane>
</telerik:RadSlidingZone>
</telerik:RadPane>
<telerik:RadPane ID="AdditionalPane1" runat="server"></telerik:RadPane>
</telerik:RadSplitter>
<telerik:RadAjaxManager runat="server" ID="RadAjaxManager">
<AjaxSettings>
<telerik:AjaxSetting AjaxControlID="RadSlidingZone1">
<UpdatedControls>
<telerik:AjaxUpdatedControl ControlID="RadSplitter1" />
</UpdatedControls>
</telerik:AjaxSetting>
<telerik:AjaxSetting AjaxControlID="RadSlidingZone1">
<UpdatedControls>
<telerik:AjaxUpdatedControl ControlID="RadSplitter1" />
</UpdatedControls>
</telerik:AjaxSetting>
</AjaxSettings>
</telerik:RadAjaxManager>