Just run the attached project and scroll horizontally to the very end several times (at least two times).
I tried disabling the column virtualization but this did not help.

This issue will be resolved with Q2 2015. 
A new virtualization mechanism for ColumnGroups will be introduced with Q2 2015. A property EnableColumnGroupsVirtualization is exposed with default value True for enabled virtualization. Setting it to False will enable the old logic. 

1. Define a custom AggregateFunction for a column
2. Group on a column
3. A calculation on the AggregateFunction is invoked
3. The Grouping.Key (of the input parameter) corresponds to the correct key
4. Edit a value on the column (having the AggregateFunction)
5. A calculation is invoked, but the Grouping.Key is "1" and not the correct key.

The group panel item image of a column with custom header is blurred

Columns with * width are not measured correctly when GridView is placed in ScrollViewer and its width is changed.

1. Select the first row.
2. Hit Ctrl-End to jump to the end of the list. 
3. Hold down the Shift key and select the last row. 
4. Scroll up and notice that everything between the first page and the last page is not selected.

* there is a sample project attached in the support thread

IsReorderable of a column is not respected when ReorderColumnsMode is different than the default one

Fixed with LIB version 2014.1.317.

Border is not correct when FilterRow is on and Column header is wrapped. Sample and Screenshot attached.

There are cells exported for the group rows, but they are empty. If you define ColumnGroupDescriptors instead GroupDescriptors, then the exported data is the correct one.

GridView ColumnGroup Header does not refresh when bound to view model

this is not related only to grid-inside-grid scenario (HierarchyChildTemplate), but also for a flat (classic) grid control. If you have a GridView and any other control (ex TextBox), you will notice that if you move focus from GridViewCell to TextBox, both

Show a tooltip when text exceeds column width.

Available in the 2017 R1 Release (2017.1.117).

The first character is lost on typing in a column with CellEditTemplate with 
RadMaskedNumericInput, RadMaskedCurrencyInput, RadMaskedDateTimeInput, RadMaskedTextInput.

When DragElementAction="ExtendedSelect" in GridView is set, there is a problem with the deselecting
behaviour. Ctrl + click no longer deselects the row.

The problem should be resolved with lib version 2015.3.1019.

Columns data gets overlapped when columns are hidden and shown again

The header row (the group headers in a GridView, or a parent row in a TreeListView) stays in the screen while scrolling until all the children rows have been scrolled.

The feature is available in R3 2017 Release of UI for WPF.
Check what's new in R3 2017 here: 
http://www.telerik.com/support/whats-new/wpf/release-history/ui-for-wpf-r3-2017

1. Scroll to near the bottom of grid.
2. Refresh the Grid, populating it with less items.
3. Should see mostly blank grid besides for bottom row.
4. If you scroll any the rows show back up.

The grips on the scrollbar's thumb is blurred on 120dpi as well as some of the borders.

As it turns out, we hit a WPF specific problem with 120 DPI. The issue is similar to the following:
http://connect.microsoft.com/VisualStudio/feedback/details/798513/wpf-dpi-rendering-issues-with-two-borders
For the time being this issue is not addressed and most probably would not be fixed. 

Provide option to enable changing the column display index when dragging group cell into the header row.

Available in the 2017 R1 Release (2017.1.117).

Let your data column have a cell style with DataTrigger which sets the Tooltip depending on the value:

<telerik:GridViewDataColumn.CellStyle>
    <Style TargetType="telerik:GridViewCell">
        <Style.Triggers>
            <DataTrigger Binding="{Binding StadiumCapacity}" Value="42055">
                <Setter Property="ToolTip" Value="THIS IS TOO SMALL" />
                <Setter Property="Background" Value="Red" />
            </DataTrigger>
        </Style.Triggers>
    </Style>
</telerik:GridViewDataColumn.CellStyle>

Initially, when the grid loads - the tooltips are set correctly. But if you edit a cell and change its value to 42055 then the background is set to Red (as expected), but the tooltip does not update.

Add an ability for the user to select a full column (the SelectionUnit should be Cell and the SelectionMode should be Multiple or Extended). 

Consider this behavior in regard with the sorting of the column.