I've never seen a comprehensive treatment of what you can and cannot pick up or manipulate with telekinesis in Diablo II, Lord of Destruction, so I started taking notes and this is what grew out of it.
Its relationship to energy shield is more than adequately covered here:
I don't propose to go over that again, nor do I propose to do more than mention its utility as a stun-locking knockback spell to hold monsters that are immune to your main attack while your buddy or merc performs the kill. If you hold down the mouse button, you can keep a monster pinned against the wall quite nicely.
All observations were made playing with the 1.11 patch in the USWest realm on Battle.net, both in hardcore and softcore games.
In the original Diablo telekinesis was principally useful for recovering your belongings from the other side of a wall while the area was still rife with monsters; you could creep back to the scene of your death and tk your things back to yourself through a wall or around a corner, equip yourself again, and wade back in to kick some butt. It was also used for opening trapped chests, tombs, and doors. You could tweak a monster with it, but it didn't do any harm, and you couldn't even smash a barrel with it.
This has mostly changed. You can smash barrels with telekinesis, give monsters a small zap, with a good chance of knockback, doors are no longer trapped, it cannot be used on anything you can wear or equip (except potions), and, most astonishing to me, you cannot use it on your own corpse. You can, however, now use it in town.
It should be noted that telekinesis requires that its object be fully on your screen. Even if you can get your pointer to reveal the object's name half-on the edge of the screen, this is normally not sufficient; usually nothing will happen, though sometimes it can result in weird behaviour too. For instance, you may be able to bring up a waypoint's menu, but clicking on your destination will do nothing.
Its behaviour is inconsistent, to say the least. This is in part due to its implementation being altered in a patch because it was so easy to abuse in the multi-player game.
It does work reliably with all container-class objects, although it will cost you a key if the container is locked.
With non-quest items, the distinction is fairly consistent and clear, and with quest-related items it always works with the container, but not the item itself, but with portals and entrances not only is the behaviour quirky in the extreme, it is inconsistent from game to game and sometimes even within a game. This may be, as Mickey has suggested, because Blizzard has different versions of the server code running on different servers; it may be also that the behaviour is execution-path dependent. That is to say, that if you have done a, b, and c, as the programmers expected, then the result will always be x, as the programme designer intended, whereas if you have done c, q, and a, the proper flag is never set and the result is an unexpected y.
I don't know enough to say for sure, and statistical observation can only tell us what seems to behave consistently and what demonstrably does not, it can never prove anything. Something has to fall up only once to blow this whole so-called "law" of gravity right out of the water, no matter how many times in the past we've seen things falling in an apparently downward direction.
Its use of mana is also inconsistent; if you try to tk an item that you cannot pick up with telekinesis, you will fail, but it will cost you mana. If you try to tk a portal you cannot use with telekinesis, it will cost you nothing.
Here's the list. Items marked with an asterisk exhibit variable behaviour between or even within games.
It works with waypoints going out & coming back home.
It works with portals going out but NOT coming back home.
It does not work for picking up quest-type items, even though these are one-to-a-customer, so to speak. Nevertheless, it does work on their containers.
Of miscellaneous items it works with the following: arrows, bolts, armor racks, baskets, bedsheets, bookcases, caskets, cocoons, corpses (except your own, astonishingly enough), crates, gold, goo piles, keys, logs, potions (incuding antidote, health, mana, rejuvenation, gas, oil, stamina), rats' nests, loose rocks, individual scrolls of teleportation and identification, skeletons, skull and bone piles, stashes (both yours and hidden), trapped souls (the ones you have to kick), tombs, undefiled graves, urns (including evil ones), weapon stands, wells, & shrines.
It does not work with these: NPCs (except the frozen Anya), doors between levels (except where noted above), gems, jewels, amulets, rings, runes, tomes of scrolls, any and all weapons and armor.
Last modified 2013-04-20