As stated above, "on attack" skills work much better in HM than in NM. Empathy, Spiteful Spirit, Visions of Regret, Insidious Parasite, etc. Hexes are good in about any situation.

Also, conditions like blind are like gold in HM. I often bring what I call, "Suicidal was Gwen," and she has interrupts, Empathy, (possibly VoR or an elite interrupt), and the ritualist skills, Blind was Mingson, and Weapon of Shadow. She'll have a tendency to run straight at warriors (thus the suicidal) but she has lots of blinding capability both around her, and on someone getting hit. up to 13 seconds of blind from the weapon spell alone. Very helpful in many situations. Also, another way to hurt melee is bring along Enfeebling Blood. There's a light sacrifice cost, but it has a huge radius and weakness really cuts down damage from about any physical damage dealer.

I also have a tendency to throw things like prot spirit or aegis on my heroes at about any point in time. Especially Necromancers. They have lots of energy and the hero AI is pretty good about chaining aegis and tossing around prot spirit as needed. (also frees up the protection monk to use spirit bond instead of prot spirit AND spirit bond, saving energy and a skill slot on their bar)

And because all enemies move faster and attack faster in HM, certain skills also get a special bonus. I'm thinking in particular about, Churning Earth which has the stipulation "Any foe moving faster than normal is knocked down" and because all enemies move faster than normal, it becomes, "any foe moving becomes knocked down". So that skill changes utility for the better in HM. Combined with the similar elite Unsteady Ground, any foe in the area of effect will be knocked down if attacking or moving. Very useful tricks. Another skill with better effect in HM than in NM is that of Reckless Haste. The enemies I believe are already at the top IAS they can have, so the hex only adds the 50% miss chance (similar to blurred vision without having to spec into water).

As others have also said, be careful of over-aggro. Just take it a bit slower when you see a group of more than 2-3. Larger groups can be quite a bit stronger than you'd expect, especially with multiple monks.

Others have also mentioned the changed priorities in targeting. Not all monks are good at healing. Hell, most pve enemy monks pretty much suck, or are part smiting. (thinking the kirin in factions, and the tormented demon monks, can't recall their name) But the eles are hellacious in hard mode. With their higher level adding the extra % of damage, as well as their increased attribute cranking up the damage, even a couple regular eles can wipe out a party in the blink of an eye. Thus they become the primary target. Also, some necromancers and mesmers are pretty nasty too. (I hate getting power spiked by a mesmer when I'm casting prot spirit. 1/4 cast interrupted? for real?)

Don't get too caught up trying to protect your team and do passive damage (hexes). You'll run into groups that simply don't attack enough to get killed, or they are simply so strong that you won't have time to make use of the passive damage. So don't forget to bring active damager dealers (nukers, sins, warriors, whatever).

Those are just some of my tips and experiences in hard mode. Hope they help somebody, somewhere.