Blender 2.56 beta (Win 7 64-bit).
Select one or more vertices in a mesh. Press translation button. Try to go down to the status area where you can input the nudge vector manually - instead the default behaviour is to move the vertices in XYZ space immediately according to your mouse movement even though no button is pressed. Not helpful. This breaks standard interface conventions of selecting something then dragging it to a new location with a mouse button pressed.
OK, so clicking the translation button twice takes you out of direct edit mode and clears the translation box so that you can input your nudge - except that sometimes it doesn't. About 20% of the time some random translation values are inserted here and this translation is applied automatically, requiring a CTRL-Z to undo it, before you can apply your own manual values. I'm guessing that it's the difference in mouse position between the two button clicks, but this should definitely be suppressed.
The translation box also behaves inconsistently. Select some vertices and nudge them. Now add another vertex to your selection so you can move that too. Click in the translation box to set your nudge, and your selection is set back to the previous set of vertices, and the translation you just entered is applied to the previous set, not the new set of vertices. To reset the translation box to apply to the new selection requires clicking the translation button twice EVERY time you change vertex selection - not user-friendly at all.
Related: I don't understand why in the interface cleanup for version 2.5 the status box giving the XYZ coordinates of vertices was removed. No doubt it's hidden somewhere, accessible with an obscure keystroke, but it is extremely useful to have onscreen by default so that separate meshes can be aligned exactly by absolute coordinates instead of by eye.
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For new users it might be diffucult to find out when things fail because you expect different behaviour, or when things fail because there's a bug.
But it would be very helpful to not report your expectations or remarks on conventions. Making Blender (better) is not what we have this bug tracker for. If you like to help, you can find a "get involved" linked on frontpage blender.org.
You should also check on blender.org the 2.57 release candidate, which has 1000+ fixes compared to the 2.56 one. The usage of the toolbar was one of the issues we've been working on. These tools there are simply mimicing a hotkey press, it's not like in Maya a permanent modal state.
The issue you noted about the vertex-selection change, which doesn't work to redo translations with, is valid yes. That we can fix.
Will assign to self.
Again, there are no conventions in 3d apps (though in this case blender does differ from most packages). It has long been a custom in blender for certain operations to immediately grab the mouse, such as rotate, translate, scale, extrude etc. Traditionally these would be fired from a hotkey and allow for very quick editing. Changing this behaviour would completely alienate any experienced users. Firing the same ops designed for hotkeys from the toolbar makes not so much sense, I agree. Personally I always use the translate manipulator, and if for example you just click on one of the manipulator handles it will immediately set the OP panel up for that axis, and you can edit numerically from there.
When you select something and then fire an OP, it will be setup for the selection at that time. Confusingly, adding to the selection will not clear the current OP, which results in this awkward (but none the less expected) behaviour. I guess selection should be an OP with its own panel itself (and I noticed it actually is in the UV editor for instance) so as to make this behaviour understandable.
So you see the whole system is consistent, but it's confusing ;)
The numeric panel has been integrated to the right viewport panel (what was it called again? It should have a visible name....) which you can access just as the old numeric panel by pressing "N".
The operator panel in the toolbar (left hand, bottom) shows the settings of the "Last redo-able operator". It is a re-do, not a repeat action.
To repeat an action on different selections, you can use the repeat option (hotkey shift+R).
The reason selections are currently not visible as "OP" (operator) here is because we still only use opengl functions for it, these are not possible to redo reliably in histories.
Long ago a developer decided to not clear the "redo" panel for selecting, so it shows a bit longer. That's indeed adding to the confusion here...
A proper solution will be to hide buttons in the toolbar for redo, but indicate the operator can still be repeated on new selections. I add this to my personal todo list, it requires a longer attention span than I can afford while going over many reports here :)
Thanks!