Can the 741's offset null pins be grounded?
This is what a 741 looks like internally: -



Bottom left are the trim pins and, as can be seen, they connect to the -Ve rail of the op-amp via 1 kohm resistors so don't mess with them, leave them open circuit if not being used or you will upset the balance of the current sources feeding the input transistor emitters.

Normally, the trim pins are used like this: -



As you can see, their recommended connection adds resistance in parallel with the two 1 kohm resistors shown in the top picture. Taking one or both to ground (normally regarded as mid-rail) will bias off those current sources.