A workaround is to remove the loading sign functionality by placing the following script at the end of the form tag

The second override is necessary only if you use the OnClientDataLoaded event to alter the data and add fields in the data object that do not exist in the server response. You need to rename the OnClientDataLoaded method call to use your actual method name.

You can find an example of both workarounds and their usage attached.

Some additional information:
- If possible, move the tiles out of the AJAX request, as this will eliminate all of the problems. Depending on the actual scenario perhaps you can make sure they are not in an update panel (e.g., position them absolutely on the page while keeping their markup out of the partial postback).
- consider moving any data formatting logic from the event handler to the template. You can define functions that format the code in the template, not only in the event. An example is available in the attached file. Alternatively, you can return the data formatted from the web service.
- consider reducing the time interval for the requests, because after the AJAX request, only 1 of 2 requests will update the tile UI.

Possible workarounds:
- switch to the Classic RenderMode of the TileList: http://docs.telerik.com/devtools/aspnet-ajax/controls/tilelist/mobile-support/render-modes
- disable DragAndDrop: http://docs.telerik.com/devtools/aspnet-ajax/controls/tilelist/functionality/drag-and-drop

Sometimes the OnClientClicked event is fired ony after the second tap, the first shows the peek template. Sometimes this can also be observed with the NavigateUrl. It is easiest seen when JS code is executed from the NavigateUrl, e.g.:  NavigateUrl="javascript:CDRequestMenu()"
This is related to the fact that there are no separate events on a touch device for mouseover, mousedown, click and mouseup.

A possible workaround is to override the CSS for tiles that need no selection abilities:
	<telerik:RadContentTemplateTile runat="server" ID="RadContentTemplateTile1" EnableSelection="false" CssClass="noSelection">
	</telerik:RadContentTemplateTile>

	.noSelection div.rtileSelectedIcon
	{
		display: none;
	}
	div.RadTile.rtileSelected.noSelection
	{
		border: 2px solid transparent;
	}

With the latest release of Firefox version 59.0, we are not able to click on tiles in a tilelist and have them navigate to the specified NavigateURL.  We verified this even on the demo on the Telerik site:

https://demos.telerik.com/aspnet-ajax/tilelist/examples/overview/defaultcs.aspx

Workaround
<telerik:RadTileList RenderMode="Lightweight" runat="server" ID="RadTileList1" ScrollingMode="None" Width="640px"
 SelectionMode="Single" EnableDragAndDrop="true"></telerik:RadTileList>
<script>
    var $T = Telerik.Web.UI;
    $T.RadTileList.prototype._handleClickAfterDragging = function (draggable, args) {
        var tile = draggable.tile,
            shouldHandleClick = this.get_enableDragAndDrop() &&
                                !this._isTouchEvent(args._domEvent) &&
                                draggable._deltaX < 5 &&
                                draggable._deltaY < 5;
  
        if (shouldHandleClick) {
            tile.set_dragStarted(false);
            if (!$telerik.isMobileSafari) {
                tile._mouseClickHandler();
            }
            draggable._deltaY = 0;
            draggable._deltaX = 0;
        }
    }
</script>

Here is a set of rules to get back the colors

		div.RadTile_Bootstrap
		{
			color: #fff;
			background-color: #337ab7;
		}
		
		div.RadTile_BlackMetroTouch,
		div.RadTile_Metro
		{
			color: #fff;
			background-color: #25a0da;
		}

		div.RadTile_Office2010Blue
		{
			color: #333;
			background-color: #dbe3ee;
		}

		div.RadTile_Office2010Black
		{
			color: #fff;
			background-color: #6f6f6f;
		}

		div.RadTile_Office2010Silver
		{
			color: #333;
			background-color: #e2e5e9;
		}

		div.RadTile_Outlook
		{
			color: #333;
			background-color: #d6e6f4;
		}

		div.RadTile_Silk
		{
			color: #fff;
			background-color: #14afca;
		}

		div.RadTile_Simple
		{
			color: #333;
			background-color: #ececec;
		}

		div.RadTile_Sunset
		{
			color: #333;
			background-color: #e88d49;
		}

		div.RadTile_Telerik
		{
			color: #333;
			background-color: #eee;
		}

		div.RadTile_Vista
		{
			color: #333;
			background-color: #eff7fc;
		}

		div.RadTile_Web20
		{
			color: #333;
			background-color: #e7f1ff;
		}

		div.RadTile_WebBlue
		{
			color: #333;
			background-color: #5d9fb7;
		}

		div.RadTile_Windows7 
		{
			color: #1e395b;
			background-color: #b8cbde;
		}

In some cases, according to a condition, after the data from a request arrives, the developer may want to prevent further requests from this same tile. This should be possible by setting the update interval to 0.

In the meantime, you can add dynamically (and remove when needed) a handler for the OnClientDataLoading event that will cancel the event and thus - the request. For example:
			<telerik:RadLiveTile ID="MyLivetile" UpdateInterval="1000" OnClientTemplateDataBound="MyLivetile_OnClientTemplateDataBound"
								 runat="server">
				<WebServiceSettings Path="Default.aspx" Method="MyPagemethod" UseHttpGet="false" />
				<ClientTemplate>
					some template that uses the data
				</ClientTemplate>
			</telerik:RadLiveTile>
			<script type="text/javascript">
				function MyLivetile_OnClientTemplateDataBound(sender, args) {
					var completed = args.get_dataItem().Completion;
					if (completed) {
						sender.add_dataLoading(preventLiveTileRequests);
					}
				}
				
				function preventLiveTileRequests(sender, args) {
					args.set_cancel(true);
				}
			</script>

Currently alt="" for the images and such a property will let the developers improve the accessibility of their pages.

The Click event is not raised at all.

At present, all events are fired when a tile is clicked, because dragging starts immediately.

This is a visible title for each group (separate from the Group.Name property), like in the Windows 8.1 Start.

If a target field is not provided in the data source and you need all tiles to have the same Target, you can use the TileCreated event to set this property. A sample is attached.

Tap on a tile to execute its navigation or rather some JavaScript. Expected behavior is for the click event to fire. Actual result is that the tile's drag is initiated - the DragStart event on the tilelist fires and the tile gets the big z-index, and you can drag it around. This behavior does not manifest when there is only one tilegroup.
Setting EnableDragAndDrop to false will alleviate this, but will remove the drag-and-drop functionality.

This issue manifests only when there is a single column of tiles, i.e., there are no more groups and no second column of tiles exists in the group. If the tile number can be expected, you can change the Height/TileRows property to create two columns. Or, split the tiles between two groups. Of course, setting EnableDragAndDrop to false will also eliminate the issue.