multiple mosfets controlling individual circuits sharing one pull up res?
Small semantic issue: A resistor going to ground from a signal that is more than ground, is called a pull-down.

The bad news is: No, one resistor for all MOSFETS means all the gates get tied together and they all switch at the same time.

The good news is: An Arduino uses a microcontroller from Atmel. All their controllers drive high and low, so if your system never goes in reset you might not need the resistors.

If your system could go into reset the internal system of the controller will go floating, allowing some MOSFETS to slowly turn on, in this case, yes you WILL need all the resistors.