Strengths:

1. Able to heal. 
2. Strong and durable enough to tank for a group.
3. Not dependent on rage like a warrior is or has to switch forms like a druid.
4. Gets the ability to summon a mount at level 40.  
5. Has abilities that allow the Paladin to be immune to attacks for a short period of time.
6. Can resurrect other players.
7. Can be very mana efficient if played right.

Weaknesses:

1. Lacks the overall damage of other classes. 
2. Both healing and tanking need to be focused on instead of trying to do both at once. 
3. Need to constantly manage blessings, seals, and auras.
4. Has a negative image on the Horde side due largely to "bubble and hearthing" (become immune to attacks and then using a hearthstone to leave the battlefield)