A priest cannot cast most heals while moving. However, almost every heal has a casting time, and if the heal gets to the target too late the result can be the death of a party member.
It takes at best 2.5 seconds, 3 without talents to get your greater heal off. If the mob is doing 2k dps and your GH is 4k normal and your tank has 10k hit points then you have to START your heal no later than the 50% point. Fortunately, most mobs (and even bosses) don’t hit that hard – especially after a tank’s armor mitigation – and all the other rates are better. That said, you STILL have to get your heal started early enough that it goes off before the target reaches zero. And it can be a pain to get the timing right when scraping the edge.
I recommend that you do a little prep to help your timing. First, learn how much health your tank (and your other party members) has. Note the point at which your normal heal will barely restore them to 100% health. Now at the start of your first few battles – and every boss battle – you do zero heals for the amount of time it takes you to cast your heal PLUS half a second. That amount is your “oh crap” (OC) point. It’s your timing mark, the point at which if you have not started your heal you might lose the player.
With practice, it can also give you an estimate for the other player’s OC point. If you know (or have asked) the total health of each player, you have your starting point. Assuming your tank is wearing plate (or has plate’s armor value), then: If they’re wearing mail the bar needs to be about 25% longer; If they’re wearing cloth the bar needs to be about 50% longer.
Example: Our tank, with 10K points, loses approximately 10% of the bar in 2.5 seconds. His OC point is when he is at about 12% health remaining. Our hunter in mail has 8K points. That same bar length is about 12% already, and because he’s in mail we need to add a quarter, making the OC point approximately 15%. Our mage with 6K health is at 15% to start, and with cloth armor her OC point is just under 25%.
I want to end by reiterating – watch the lag. If you start at 150, and midbattle something causes it to spike to about 600, your spells will reach the server just under half a second later — which means that if you cast a 2.5 spell 2.8 seconds before the tank would die, the server receives “spell complete” at the 3.1 second point or 0.3 seconds too late.