i believe the only caution you need to have is knowing that you do not have the ability, the time, or the energy to pray for EVERYTHING, and you arent called to.
many people you never knew or heard of die from disease and murder and things around the world, was it becuase you didnt pray? no.
there isnt time enough in the world for you to pray for all the needs that exist. (though i believe praying that Gods will be done on earth is very effective in meeting needs we dont even know exist)
just like you do not have the time, energy or funds to assist every christian venture that is asking for your support.
telling someone you cant give yourself to their venture isnt wrong.
and not personally praying for everything isnt wrong either, its not possible. sometimes those people must pray for themselves and God holds THEM responsible for THEIR life.
just remember this, Jesus was once in a house, and a crowd was growing outside. and the disciples and others expected him to stay and minister becuase there was an apparent need.
but Jesus did not, he left this crowd of people who wanted him so badly behind and went on to another city.
and Jesus said it was becuase of the "Purpose" on his life.
potential does not equal purpose. he had do what he was PURPOSED to do, not what he could POTENTAILLY do.
one day you may be accused of failing to pray, witness, give money, because someone needed it, though dont let it make you condemned for not doing enough.
you must realise that what is important is that you be LED BY GOD, in what to pray for, not just pray becuase someone appears to need it.
it is more important to be LED by the holyspirit in prayer time, than to try and hit all the needs you can think of for other peoples sakes.
you only have a certain amount of grace, or power. and God has given you given thing to watch over. and your called to watch over that thing. not the whole world.
like paul said THIS ONE THING I DO...
just remember that God is in control... and hes dealing with those situations if those people are seeking him, and you may not be the one hes using to pray etc.
you can rightly pray for anything unless God tells you not to (and he does that sometimes) but make sure you dont spend your time on things just because you THINK YOU NEED to pray for it, becuase you can waste the limited amount of time and energy you have and miss the thing God wanted to do in your life. some people even neglect and never fullfill their own callings becuase they spend themselves completely on other poeples callings.
every man must bear his own burden.