When you use new pads on old discs the pads will be perfectly flat/square..the old disc wont be as it will have many thousands of miles use hence its worn..it will take a while for the pads and discs to wear in together.

You may also find the disc is no longer 'true' and runs out causing it to drag if the caliper has been stuck before/overheated causing it to warp.

Personally id strip the offending brake down and re clean it with brake cleaner and silicone/red rubber grease on any rubber/boots and copperslip in the pins and back of the pads...AND I'd sort the spongy brakes asap.