Transfer update, definitely.
Match engine issues, statistic issues, registration issues... etc... should fix your saved game, but like FrazT says, you might have to restart for some of them to take effect.
One example I am thinking of is Chairmen personalities. A lot of these guys are proper idiots on the game, selling your best players for only 10-25% more than their value. If this is pre-programmed into their personality you'll have to restart a game for this fix because of how the game works. If it's a problem in the game code itself it should be fixed in your saved game.
For the record, this example DOES happen in real life, and
IMO should remain, but the decisions should be based around much higher "too good to turn down" limits.