The 1st-level Sor/Wis spell obscuring mist [conj] (PH 258) says that its
vapor obscures all sight, including darkvision, beyond 5 feet. A creature 5 feet away has concealment (attacks have a 20% miss chance). Creatures farther away have total concealment (50% miss chance, and the attacker cannot use sight to locate the target).
First, that means a creature can see into its adjacent squares... not well enough to shank a conscious and mobile foe in the kidney, but well enough to distinguish ally from enemy, and, presumably, adjacent solid ground from adjacent empty space. Second, keep in mind that
creatures don't, RoboRally style, commit to all their movement before making it; a creature needn't plot a course then take that course, heedless of his new knowledge of battlefield conditions. Instead, the decision either to continue to any other legal square or to stop moving comes after both assessing the effects of having entered the new square and determining what new information about the world entry into the new square has provided.
Hence a creature enveloped in the vapors created by an obscuring mist spell should no more accidentally fall off a cliff than he should accidentally throw himself into a wall. While that would be hilarious in Teenagers from Outer Space and a possible pedestrian fatality in Car Wars, that's not really a thing here.
That's not to say this isn't tactically dangerous, and, really, the spell obscuring mist if cast on plateau—unless one side has a way to see through the vapors that the other side lacks—should bring the fight to a standstill until the spell's duration expires. Neither side should want to risk their combatants being bull rushed off a cliff. (Unless one side's comprised of kobolds.)
If the fight's on a plateau in total darkness yet one side can see through the darkness and the other can't, the DM can save some time and just narrate the battle: The side that can't see loses. While the blind side flails about, the side that can see takes their time, pelting the side that can't see with free rocks launched from free slings until either every creature on the blind side dies or dawn. (For high-level characters, this may very well be dawn.)
More to the point, nothing stops a creature from entering a square of empty space from a square of solid ground, but if the creature lacks a fly speed the creature will fall. Prior to this expedition against the Shadow-spewing Gnolls of the Cliffs of Eternal Night, everyone put ranks into the skill Climb, right? Because
It’s practically impossible to catch yourself on a wall while falling. Make a Climb check (DC = wall’s DC + 20) to do so. It’s much easier to catch yourself on a slope (DC = slope’s DC + 10).
Of course, much easier here means not totally impossible. The description of hills terrain, the main source of information on slopes and cliffs, says the DC for scaling a cliff is 15. Thus, by extension, a creature who is blinded on a cliff and moves into a square of not-cliff can make a Climb skill check (DC 25) to catch himself. (It probably goes without saying, but rare is the visually-impaired mountaineer.)
Two Possible House Rules
First, in an attempt to locate foes
A character can make a touch attack with his hands or a weapon into two adjacent squares using a standard action.
A reasonable house rule allows a blind (or sighted!) creature to use the same method to determine if one or two adjacent squares are safe for entry.
Second, movement while blinded costs 2 squares per square traversed, but whether this is due to the care one must take to move carefully, a lack of proprioception, mischievous earth spirits, or something else goes unstated. If the DM interprets this as a creature's natural, reckless sense of being able to navigate wherever he wants being blunted by his sightlessness, a reasonable house rule has a blind creature make a Balance skill check when about to enter a square that the creature could identify as dangerous with another sense (e.g. the heat of lava, the stench of acid, the sound of rushing water, the vertiginousness of a sheer drop). Success means the creature gets an idea of the danger present in the square and may either continue moving into that square, pick a different square into which to move, or stop moving altogether. Failure means the creature enters the dangerous square. The DM and the terrain must dictate this Balance skill check's DC.