At that moment, I have a level 70 Paladin so I know what about I am going to talk about and know most of you probably have a 70 pally too so this is just my opinion.
Paladins doing quests will only get into difficulties if you stretch your limit too high if you are say a level 25 pally and try to take a 28 down - make sure you have the gear and full mana, additional buffs help and so on. Even though you can heal, make sure toward the end of the fight you still have mana left incase another mob comes running for you.
Many times I have had a mob 3 level above me come fight me, once killed another and another. My longest chain was around 6 mobs one after another, any other class would quite simply die, maybe not a shaman. Conserve mana - no mana = death. You do have LoH - life saver. BoP can help but you need mana to use it - and even then you have to wait a whole minute until you can cast the other. It can get tricky.
In a raid, paladins are required to be either a mani or back-up healer. Why? Quite simple pallys heal the raid - priests and druids heal the tanks and can offer support to the raid. This was the case certainly pre TBC. Post TBC we are main / support healers - always keep the man to your left and right alive - this way you will see more end game instances and get good gear fast. Build yourself a reputation, always strive to heal better!
All I care about is mana, intellect, mana regeneration. I use mana food, mana oil; if I get agro
Shield, stun and judge with light and put in a few hits. Maybe because the tanks I play with are my guild tanks. They expect me to heal them at all cost and I expect them to protect me at all cost and we do it because we care for each other and for the guild's progress. It makes all the difference when those around you are reliable. They fill you with joy and pride and they make the whole game better.
One thing worth mentioning is choosing kind people around you, smart and fast. If you make a mistake they will correct it, and if the do it right you will never make that mistake again and you will never let them down. Choose people who believe that you can achieve your goals.
It seems understandable that paladins always talk about little mana and so on. I get my mana from a lot of mana regeneration gear, a lot of intellect. Even when I needed to wear a robe, I didn't mind since the intellect and stamina were amazing on it, and intellect, healing and mana enchants. I use as my healing weapon "hand of Edward the odd" with a +22 intellect enchant. Intellect gives us spell crits.
I have tanking gear, and I find that a paladin really rocks when tanking undead. I add plus to defense and the tanking set from school is really good with some soul forge and some gear from Zul'gurub. What I find amazing though is trinkets. They can be such a bonus. I suggest to any paladin who is going to be an end game holy specc to go for talisman of ascendance and dark moon card: blue dragon. One gives bonus to healing the other regenerates 20% of my mana lost in casting, during casting.
Paladins can heal and can be a good DPS, they can do both successfully the only thing is to avoid being caught in the middle. The DPS when fighting undead is outrageous. But only if the have the right talents. Paladins are holy warriors. And they can do it well.