I've decided to check every commercial Wolf3D and SoD level to find out when a three space move can cause a problem (block off an item or path). And I'm only listing cases where (intended) movement of two spaces does NOT block anything off:
Wolfenstein 3D (all coordinates from MapEdit):
Episode 1: No issues can ever be caused. Hooray for shareware!
Episode 2: No issues once again, Eisenfaust is a winner!
Episode 3: Level 4 - first problem in the game. (34,57) will block a medkit if it goes three spaces.
Episode 4: On Level 2, (18,33) will block a treasure if it goes three spaces, unless you already got said treasure through (20,37).
Episode 5: On Level 2, (52,40) goes over an ammo item if it goes three spaces. On Level 4, (24,43) stops on a medkit if it goes three spaces. On Level 5, a treasure is blocked with (8,49) going three spaces. Another treasure is blocked by (37,12) on Level 8 which Chokster mentioned.
Episode 6: Level 2 has an extremely critical problem with (19,51) as described previously. And, within that chain of secrets, (12,32) will block off an extra life. On Level 8, (40,23) will block off a treasure, and (52,58) will stop over top of an ammunition clip.On Level 9 (boss), (16,47) will stop on a medkit. Finally, on the secret level (10), (52,49) will stop on an extra life but make the other two attainable, while two spaces blocks off that entire section of the secret.
Spear of Destiny (note: only covering the first (original) mission for now, not the Lost Episodes)
On Level 4 (already mentioned by Chokster) - (23,46) stops on a treasure.
On Level 11, (22,53) will stop on a treasure and (26,9) will stop on a one-up if not already collected
On Level 12, (8,58) will block off the secret elevator (and you can get there through another combination, but have to use (8,58) to get 100% on everything and also the secret exit).
On Level 13, (48,31) will land on a treasure unless you already picked it up.
On Level 15, (32,49) will stop on a medkit.
On Secret Level 1 (Level 19), (50,21) will land on a medkit.
Note: I don't have nearly enough time to examine Secret Level 2 (Level 20) - just waaayyy too complex of a level with far too many secrets to check them all.