I'm building a scoreboard with 9 separate digits. I don't want to overload the shift registers so could I simply control the LEDs with a n-mosfet? I'm unsure how the gate latch works, if it goes +5v or 0v and if enough current produced my the register will allow for steady, continuous latching.
You can drive a N mosfet from a 595 just fine 
It's just like driving a mosfet from an Arduino pin. Use logic level mosfets is the load is high.
Do you mean a scoreboard with large 7-segment displays.
If the displays are common anode, and drawing <100mA, then swap your 74HC595 chips for the TPIC6B595.
Same shift register, but with buildin mosfets.
Sparkfun has another member of this TPIC family on a breakout board.
Leo..