I never noticed this before, but when Dominion puts out my new hand, the cards are in random order...from, of course, the top 5 cards in my deck. I don't know why I have been assuming--for years!!!--that the card that had been on top of my deck is at the far-left of the 5 cards. Or, is at the far-right. But no. Yesterday was the first time (at least, when I was paying attention) where my last move in a turn was "Topdeck Caravan." But, Caravan was 2nd from the left when I got my new hand.
Should I/we care about this? I have to admit that I can't think of a situation where this is important. :)
Yeah, this is a pretty annoying problem. There are many situations where card order matters and the game does not prompt you to pick card order (for example, when topdecking multiple cards), or deciding what order to discard cards (only the last card discarded should be visible), etc.
When you discard cards "by choice" (say due to Milita), the last card picked will be the last card discarded (and thus observed by the opponents).
While topdeckoing, the cards are topdecked in the order clicked. So with Ghost Ship, the card you click last will end up on top of the deck.