When one activates this effect of smiting evil/good, should other characters be able to see it IG? for example when smite evil is used would divine light surround itself around the paladin's weapon and flash brightly as it makes contact with the evil-doer? and would smite good have darkness warped around the blackguard's weapon and writhe it's way into the good guys? Or is it just seen as a lucky hit when left unexplained by the PC who uses it?

IIRC, there's a special impact VFX associated with Smite Evil/Good. Other than that, I want to say no, but that's just my personal opinion.