How high can pull up/down resistances be?

The value of a pull-up or pull-down resistor is limited by the leakage current of whatever it is pulling.

For instance, say you have a 100K pull up resistor on a mosfet gate connection, and the mosfet has a gate leakage current specification of +-10uA. Your 100K resistor may only pull it up to around 4V due to this worst case leakage current.