http://iscoresports.com/

I recenctly took all of my team's games that where scored on paper and put them into iScore. For each game I set the scheduled date and time, as well as start/end date and time for the games(e.g 5/3/11 8:30PM start, 9:30pm end). When I look at a player's card and stats it shows today's date for when the game occured and not the date the game actually happened.

you have stumbled on a small quirk in the current version of the software.
FTM knows about it and reportedly will correct in future version.
Until then, there is a manual workaround to fix it. and i will try and describe below

basically, the payer card date field does not automatically update if you edit the game start date after a game is completed, .. to update player card to current date value in start data field, you need to force a recalc of game stats, by either end game undo/redo or stats recalc button.

caveat...
the player card has two fields that often contain date info, one is the game title and the other is associated with the stats. , below is how to refresh/edit each

1) Game Name Field in Player Card Stats... (right most column of stats in player card)
the Game Name includes the date the game was created by default, to override/edit, go to game info screen (game manager > select game> ) and edit the name in to the top field (hit done on keyboard, to save). back/exixt. the player card will update automatically

2) game schedule start and end date (game manager > Game info Screen)
As you already, know the game start and game schedule and game end date , all can all be edited on the game info screen , using the date picker wheel. If done before the game scored all is ok, but if done after the game has been scored, may need a manual "refresh"

3) the stat date in player card (left date field in player card - and i suspect the column you have issue with).. the date field in the stats on player card does not automatically update when the game start date is edited in the game info screen after a game is final. to do this you need to
a) Game Manager > select game, > play, ("game over") > hit undo > redo >, exit.
b) recalc stats. game manager > select game > ("game info screen) > tap a stat category (eg home/visitor batting/fielding/pitching stats) > tap upper right "recalc" button.
i) if you have manually overridden any stats choose "no" to reatin them,
ii) if you have not done any manual stats override, safe to hit yes, to recalc all

the date on player card will now correspond to start date (not schedule date or end date)

This should fix the player card date fields in the current version, future version should fix this more automatically.