The very bottom of CellMargins is missing

There is a straightforward way to set CellMargins to be zero:

DialogInput[
 DialogNotebook[{ExpressionCell[Pane[RandomImage[], ImageMargins -> 8], 
    CellMargins -> 0]}]]

Instead of ImageMargins we can rely on CellFrameMargins:

DialogInput[
 DialogNotebook[{ExpressionCell[RandomImage[], CellMargins -> 0, CellFrameMargins -> 8, 
    CellFrame -> True, CellFrameColor -> None]}]]

On my system (Windows 7 x64) with Mathematica 10.4 the CellFrameMargins method gives more accurate results than ImageMargins (compare the screenshots):

DialogInput[
 DialogNotebook[{ExpressionCell[Pane[RandomImage[], ImageMargins -> 1], 
    CellMargins -> 0]}]]

DialogInput[
 DialogNotebook[{ExpressionCell[RandomImage[], CellMargins -> 0, CellFrameMargins -> 1, 
    CellFrame -> True, CellFrameColor -> None]}]]

---

From your second example in the question I believe that this behavior is determined by the WindowSize -> All Notebook option which makes the window

large enough to fit all visible contents

(emphasis mine).

It seems that FrontEnd crops CellMargins because they "aren't visible". But with this explanation the inconsistency is that it crops them only at the bottom but not on the right even if we switch off displaying of the cell bracket:

NotebookPut@
 Notebook[{Cell@
    BoxData@ToBoxes@Pane[RandomImage[], ImageMargins -> 0, FrameMargins -> 0]}, 
  WindowSize -> All, WindowElements -> None, ShowCellBracket -> False, 
  WindowFrameElements -> {"CloseBox"}, CellMargins -> 10]

If we add another cell we can see that CellMargins are actually respected:

NotebookPut@
 Notebook[Table[
   Cell@BoxData@ToBoxes@Pane[RandomImage[], ImageMargins -> 0, FrameMargins -> 0], {2}], 
  WindowSize -> All, WindowElements -> None, ShowCellBracket -> False, 
  WindowFrameElements -> {"CloseBox"}, CellMargins -> 10]

So I'm inclined to think that we have a bug in handling of the WindowSize -> All option: the expected behavior for this option is to treat CellMargins as visible contents and make the window to be sufficiently large to include the whole CellMargins.

I gave up looking for neat solution. Here's brute force.

Since the bottom CellMargins are not respected then let's not use any! :) We can use Pane and its ImageMargins to take control over padding.

DialogInput[
   DynamicModule[{},
      Pane[RandomImage[], ImageMargins -> 8],
      Initialization :> (SetOptions[EvaluationCell[], CellMargins -> 0])
   ]
]

So in general instead of RandomImage[] put the code you would have used in DialogInput.

It really expects that you have some buttons along the bottom.

DialogInput[Column[{Pane @ RandomImage[], Button["OK", DialogReturn[0]]}]]

but you can do it this way

DialogInput[Column[{Pane @ RandomImage[], ""}]]

Update

I Think it looks better with the bottom margin a bit larger than the top, but if you are being picky about equal margins, try

DialogInput[Column[{Pane@RandomImage[], ""}, Spacings -> 0]]