Well, there's basic stuff like spamming right click on enemies after you use an ability, that way your hero won't wait for the full spell animation and you end up throwing out a few more autoattacks in a fight. It really adds up if you do it consistently.
You can drag enemies close to the resurrection stones so that they are right outside it's radius and you can get the mana/healing so you can spam your abilities more.
Kill every barrel, crate, ancient bookshelf etc, they have goodies.
When crossing a spiketrap with an elevator, wait for it to go down, then spamclick to move to the other side, as soon as it rises you will start moving, and you won't fail it.
Bosses don't heal too quickly, so if you're not going to kill him, you can run back out and heal, then return and kill it. Kind of cheap, but I did this a lot when I was playing single player, as I was running a Death Knight built for selfhealing, it didn't have much damage outside of it's Q ability.