Provided the motherboard supports the cpu you should have no problems upgrading, much like a standard desktop motherboard as long as it supports the cpu its should be nothing more than a quick switch.
The current dell bios for the Inspiron 1501 fixes only an "erroneous bad battery message during post" you can find that here:
Drivers and Downloads
Althought be wary of DIY upgrades if I am not mistaken as such will void your warranty from Dell, although I am not 100% sure of that.
I would also like to refer you to this thread it might have some useful information:
Dell Inspiron 1501 CPU Upgrade
Good luck and welcome to HWC

,
EE