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I understand that magic find increases the chance of an item being "upgraded" from a white to blue, blue to yellow, yellow to orange/green, but is there anything, like high monster power, that affects the "quality" of an item, like a weapon's damage?

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Enabling Monster Power in Inferno causes all monsters to be level 63. Since item affixes are generated based on monster level, this means that any item can now generate the best possible affixes. You also have the best chance of iLvl 63 items spawning, which have the best base stats. Without Monster Power, you wouldn't get that until Act 3.

Otherwise, no. Monster Power has no impact on item rarity beyond the magic find impact.

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No. The only improvements from playing at a higher monster power is increased chance for magic/gold find, and a increased chance of a regular white monster dropping an additional item when killed.

Magic Find also does not improve the 'quality' of a weapon modifier (i.e. adds 1000 damage instead of adds 100 damage), but it does have an affect of the number of affixes on an item may have. The higher the MF%, the more likely it is for an item to have more affixes (i.e. 6 instead of 4).

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Monster power gives you additional :

  • Xp
  • Magic find
  • Gold find
  • Bonus item (The chance to drop a bonus item in addition to magic find, in inferno)

From the d3 official blog: http://us.battle.net/d3/en/blog/7540457/

Starting at MP1, each level of Monster Power will increase monster damage and health by a scaling amount depending on difficulty. To reward your audacity, your hero will receive bonuses to experience, Magic Find, and Gold Find (which will stack above the 300% cap). For Normal, Nightmare, and Hell, the bonuses look like this:

enter image description here

In Inferno, in addition to increased experience, Magic Find, and Gold Find, whenever a monster dies and drops an item normally (whether it be gold, a potion, or a piece of gear), the monster also has a chance to drop an additional bonus item. The chance to drop a bonus item will scale up with each MP level as detailed in the table below.

enter image description here

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I agree with everything you have answered but i have to seperate the affixes that must be rolled for a drop with the Values the games rolls for those affixes .. There is this rumor that bigger the MP is better the rolls for values of those affixes are.. you can't confirm it easy because you need a very big testing pool ... My personal feeling is that harder the mp is better the stat values of the affixes are.. But even if the rolls of values are slightly better on bigger MP the time it gets for you to get items in bigger MP doesnt poise the quantity you get in less MP. so i believe farming must be done in the MP you do faster..

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At any Monster Power above 0, all monsters are level 63, and all have the exact same chance for affixes. The rumor that higher MP gives better affixes is exactly that, a rumor. –  Frank Jan 7 '13 at 17:58
    
dude seperate in your mind the affixes from the values those affixes take... every affix has a range of values that can be rolled. the Affixes might be the same for all the level 63 but noone says that the values those affixes take will be the same.. if you find me an official answer of blizzard that will say that the value roll is the same for all levels ill agree.. but till then seperate the affix roll from the value roll –  Excadrix Jan 7 '13 at 18:17
    
Affix tiers is exactly what I'm talking about. There are two rolls made when a monster drops an item: The affix roll, which determines what affixes the item will have, and the value of that affix. Monster level is what affects the affix roll, NOT the value of the affix, which is determined from the minimum and maximum that affix can have. –  Frank Jan 7 '13 at 18:23
    
and how this is different from what i say? –  Excadrix Jan 7 '13 at 19:20
    
You're implying that higher monster level = better values, which is incorrect. MP 1+ = all monsters are level 63. All monsters from Act 3/4 at MP 0, to any monster at MP 1+ have the exact same chance to roll the best affix values, because that's the best they're going to get. After that, it's all up to the RNG. –  Frank Jan 7 '13 at 19:24
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