I would die laughing if the Doctor got into TNG and used the sonic to make Data do weird things. :P
That, and it might be funny if pointing it at Odo on DS9 makes Odo liquefy. Cue the Doctor going "Whoops...ah, sorry!"
I think it could disable handheld weapons like phasers, but not whole starship weapons systems. And I imagine it could seriously mess up/KO a Borg drone.
All kidding aside, I think the sonic screwdriver is a great tool. It doesn't work on wooden things. It's never solved the plot although it has led TO the solving of a show's plot. I personally think it's fine.