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.

When items are data bound, their IDs should be stored in the ViewState so the next time they are recreated (upon a postback), they have the same IDs, so postback events can be raised.
Also, when a new datasource is provided to the tilelist, keeping track of the IDs will let the control create tiles with the same IDs that were used instead of incremental ones.
Both of these will prevent the tiles ID change in the first two page loads after a DataBind() call.
Note that this applies only for the case when AppendDataBoundItems is false; when it is true new datasources should only add items.

A workaround is to set IDs to the tiles manually when they are created (this can be done with a simple counter variable).
To accommodate for rebinding the tilelist, its controls collection must be cleared prior to databinding as a workaround.
A sample is attached that shows these in action.