seeing someone elses cards is not really that important in cash poker, it does depend on your own house rules though whether you have a face-up rule for all-ins but as I previously stated that is just wasting time and rake, those who wish to claim the pot should table their cards, your cards are your claim to the pot, I think there has been too much emphasis on the fact that the player is all-in in this thread, as Nick says if he is in the hand he would table his hand and wait for a further claim to the pot to arrive, which is fine, or he would wait for the last agressor to table if it was in that betting round.
For tournaments, where there is no bet on the river it is clockwise by pots order (for example players contesting pot 3) would table first, followed by pot 2, followed by pot 1, where there was action on the river the last agressor would table first. It does also state "A player with a probable winner is encouraged to table without delay (slowroll)" so that should also be considered.
In Cash though, dependant on your house rules, it's different, throw your cards in the muck if you want to surrender, table them if you want to claim the pot, is a crude but effective way to consider showdowns, For example, two players go all-in pre-flop everyone else folds, do you enforce a showdown here? or do you do what we do, simply deal the board out and then wait for someone to claim the pot? The latter is faster and generates more rake per hour, I don't think Face-up for all-ins should apply whatsoever in cash games - it's cash and it's more or less only the current hand being played. In Tournaments it's the whole game that matters on each and every table from start to finish.
Regards
Stuart