Hardcore mode adds some sense of realism into the game. The most important factors to remember is using Stimpaks when you start a fight where you expect to be hit (as the healing effect is NOT instant anymore), stock up on Doctor's bags and/or poultices to heal limb damage and watch your physical needs (drink water, eat and sleep regularly).
Do NOT expect to Stim-tank a Deathclaw anymore. If it cripples your leg, you are probably going to die horribly.
This also means that you need to be CAREFUL with mines, grenades etc, as crippled limbs are harder to fix: Doctor's bags are heavier, which means that you can't carry a ton of them around (and also harder to find than Stimpaks). Did I also mention that ammo has weight in HC mode? Bear that in mind if you suddenly have an encumbrance problem and can't find the source. Finally, you need to be careful with your companions, as they can and will die permanently in this mode. So be sure to check on their status before you overwrite your save.