There are two reasons for pullup/pulldown resistors.
1) If a chip has i/o on the same pin, you can exceed its current output rating if it is tied to ground and it is inadvertently enabled as an output. With most modern chips this is a non-issue, but 20 years ago it was a good way to destroy one.
2) During prototyping and early production, or during test, it may be useful to force the state of the input either with cut-and-jump mods or with a test fixture.
If neither of these apply, then hard-wire the input to ground or vcc.
If either apply, then use a separate resistor per pin.
Check that the chip does not already have a built-in pullup or pulldown. An external resistor may not hurt, but it won't add any benefit.
Tieing multiple inputs together and then pulling them up or down together seems like a confused operation with all the disadvantages and none of the advantages.
DspDad