Steps to reproduce:
1.Create a Telerik Grid with SelectionMode=@GridSelectionMode.Multiple and a GridCheckboxColumn to select/unselect the rows. 
Also, bind the selected items to an IEnumerable collection and display the selected items in a <ul>
2.Click on Row1's checkbox - It selects the row, but not checking the checkbox
3.Click on it again- Now it unselects the row, but the checkbox is checked.
4.Click on the SelectAll checkbox in the grid header - It selects all rows, row checkboxes are checked, but the SelectAll checkbox in the grid header remains unchecked.
5.Click on the SelectAll checkbox again - All rows remain selected, row checkboxes remain checked, The SelectAll checkbox is now checked.
6.Click on the SelectAll checkbox again- All rows are unselected, row checkboxes are unchecked, The selectAll checkbox remains checked.

Another issue is, corresponding row checkbox remains checked on moving to next page eventhough the row is not selected. 
For eg,
1. a grid of 20 rows displays 10 items per page; Row 2 is selected and checkbox is checked
2. Move to page 2 - Row 12 checkbox is checked (but row 12 is not selected)

Please note that this discrepancy is only when using a checkbox column, otherwise the grid selection using Ctrl + Click works as expected.

Attached Screenshot of one of the issues

On clicking Row 2 checkbox again, result below