We can use ASP.Net validation controls with SharePoint DateTimeControl to validate the date. Following code snippet demonstrate the usage of ASP.Net validation control to accomplish the following validations on the SharePoint DateTimeControl:
1) Required field validation
2) Valid date validation
3) Date compare validation

<table>
   <tr>
       <td>
           <SharePoint:DateTimeControl ID="dateTimeStartDate" runat="server" DateOnly="true"></SharePoint:DateTimeControl>
       </td>
   </tr>
   <tr>
       <td>
           <SharePoint:DateTimeControl ID="dateTimeEndDate" runat="server" DateOnly="true"></SharePoint:DateTimeControl>
       </td>
    </tr>
    <tr>
       <td>
           <asp:RequiredFieldValidator ID="RequiredFieldValidator5" runat="server" ControlToValidate="dateTimeEndDate$dateTimeEndDateDate" ErrorMessage = "* Required value" Display="Dynamic" ></asp:RequiredFieldValidator>
        
          <asp:CompareValidator ID="CompareValidator2" runat="server" ForeColor="Red" ControlToValidate="dateTimeEndDate$dateTimeEndDateDate" Type="Date"
              Operator = "DataTypeCheck" ErrorMessage="* Please enter an valid date." Display="Dynamic" ></asp:CompareValidator>
        
          <asp:CompareValidator ID="valDate" runat="server" ForeColor="Red" ControlToValidate="dateTimeEndDate$dateTimeEndDateDate" ControlToCompare = "dateTimeStartDate$dateTimeStartDateDate" Type="Date" Operator="GreaterThanEqual" ErrorMessage="* Please enter End Date Greater or Equal to Start Date." Display="Dynamic" ></asp:CompareValidator>
       </td>
    </tr>
</table>