When the SearchBox is on the right side of the screen and the dropdown width is larger than the SearchBox width, the dropdown goes outside the viewport:
Actual: https://www.screencast.com/t/4SoNcRCj
Expected/fixed: https://www.screencast.com/t/smfPgy767M

Workaround: 

<script>
    function OnClientLoad(sender, args) {
        sender._dropDown.on({ "reflowed": sender._onReflowed }, sender)
    }

    Telerik.Web.UI.RadSearchBox.prototype._onReflowed = function () {
        var that = this;
                       
        var $animationContainer = $(that._dropDown._animationContainer);

        if (that._enableScreenBoundaryDetection) {
            var availableSpace = that._dropDown._getAvailableSpace();
            var tableWidth = $(that._innerWrapElement).outerWidth();
            var dropDownWidth = $animationContainer.outerWidth();
            var overflow = dropDownWidth - (tableWidth + availableSpace.right);

            if (overflow > 0) {
                var left = parseInt($animationContainer.css("left"), 10);
                var newLeft = Math.max(left - overflow, left - (dropDownWidth - tableWidth));

                $animationContainer.css("left", newLeft);
            }
        }
    }
</script>
<telerik:RadSearchBox runat="server" ID="RadSearchBox1"
    DataTextField="ShipName" OnClientLoad="OnClientLoad" DropDownSettings-Width="500px" DataValueField="OrderID">        
</telerik:RadSearchBox>

Validation is not implemented for RadSearchBox.

You can find attached an example that emulates validation of a search box through a dummy textbox and validators attached to that dummy textbox.

In certain scenarios time between clicking (focusing ) the SearchBox and being able to interact with it.

The issue is iOS7 / Safari specific

RadSearchBox.Focus() doesn't work in Internet Explorer. It works correctly in different browsers (Firefox, Chrome). Attached project shows the problem. 

There's a problem with radSearchbox inserted in a radWindow contenttemplate.
On First show  then inputText width is equal to 0 until a contextitem is selected or a button pushed . (test on ie10 firefox and chrome)


code example :

  <telerik:RadWindow runat="server" ID="RadWindow1" Modal="true"     AutoSize="true"
        Behaviors="Close,Move">
        <ContentTemplate>
         <telerik:RadSearchBox ID="RadSearchBox1" runat="server" Width="350" SearchContext-ShowDefaultItem="False"
                        OnClientSearch="onClientSearch" OnClientButtonCommand="onClientButtonCommand"
                        ShowSearchButton="false" Skin="Default">
                       
                        <DropDownSettings Height="150" Width="300" />
                        <Localization LoadingItemsMessage="recherche en cours....." DefaultItemText="Saisissez le nom du point ici" />
                        <WebServiceSettings Path="PointDeTournee.aspx" Method="GetResults" />
                        <SearchContext>
                            <Items>
                                <telerik:SearchContextItem Text="POI" Key="1" ImageUrl="../Img/POI/Special_Divers-Bl.bmp"  Selected="true"/>
                                <telerik:SearchContextItem Text="PA" Key="2" ImageUrl="../Img/POI/PA.bmp" />
                            </Items>
                        </SearchContext>
                    </telerik:RadSearchBox>
          </ContentTemplate>
    </telerik:RadWindow>