Q:

Was the Noah flood global or local? 

Many criticize Bible because it talks about Global floods at the time of Noah.  They think it is a big mistake.  Muslims believe that Noah's floods were local.  They think Quran corrected that stories which exists in the Bible.  However from what I understand, Noah's flood are global in Quran as it seems.  It can be seen from the following verse
Quran 23:27

So We inspired him (with this message): "Construct the Ark within Our
  sight and under Our guidance: then when comes Our Command, and the
  fountains of the earth gush forth, take thou on board pairs of every
  species, male and female, and thy family- except those of them against
  whom the Word has already gone forth: And address Me not in favour of
  the wrong-doers; for they shall be drowned (in the Flood). 

Quran 11:44

Then the word went forth: "O earth!  swallow up thy water, and O sky! 
  Withhold (thy rain)!"  and the water abated, and the matter was ended. 
  The Ark rested on Mount Judi, and the word went forth: "Away with
  those who do wrong!" 

Noah builds the ark and collected all kinds of specie in pair, then the ark lands on a mount.  Wouldnt this mean the floods were global.  This link says says

Apart from those who boarded Prophet Nuh's (as) Ark, the entire tribe
  was drowned.  The dead included the Prophet's son who thought he could
  escape by seeking shelter on a mountain. 

So why was it not global flood.  If you consider that Earth was considered flat at that time, this makes perfect sense.  My other argument is one needs only about 100 ft of flood water (esp in those times) to destory a particular tribe.  We are talking about Mountains here.  

A:

Look at the verses in the Quran in reference to the flood:

We sent Nuh to his people and he remained among them for fifty short
  of a thousand years; yet the Flood engulfed them while they were
  wrongdoers. ( Qur'an, 29:14)
We sent Nuh to his people: "I am a clear warner to you.  Worship none
  but Allah.  I fear for you the punishment of a painful day." ( Qur'an,
  11:25-26)
But they denied him so We rescued him and those with him in the Ark.
  And We drowned the people who denied Our Signs.  They were a blind
  people. ( Qur'an, 7:64)
So We rescued him and those with him by mercy from Us, and We cut off
  the last remnant of those who denied Our Signs and were not believers. 
  (Qur'an, 7:72)
So We opened the gates of heaven with torrential water and made the
  earth burst forth with gushing springs.  And the waters met together in
  a way which was decreed.  We bore him on a planked and well-caulked
  ship. ( Qur'an, 54:11-13)
We revealed to him: "Build the Ship under Our supervision and as We
  reveal.  When Our command comes and water bubbles up from the earth,
  load into it a pair of every species, and your family-except for those
  among them against whom the word has already gone ahead.  And do not
  address Me concerning those who do wrong.  They shall be drowned." 
  (Qur'an, 23:27)
It was said, "Earth, swallow up your water!"  and, "Heaven, hold back
  your rain!"  And the water subsided and the affair was concluded and
  the Ark came to land on al-Judi.  And it was said, "Away with the
  people of the wrongdoers!" ( Qur'an, 11:44)

As we can conclude from the verses, the flood was local because it talks about his people and the boat was built to take refuge of every species from that location and flood was localized in Quran nothing to indicate it was universal.  You can't just quote 2 verses and make conclusion, you have to quote every single verse in relation to noah and the flood and if you read all of it in context then it indicates a local flood, and it never mentions every single humans from the world but those who denied his signs. 

A:

The flood was local because it was a torment to those who denied Noah's (AS) preaching.  Noah(AS) was close to Adam(AS) which indicates that at that point the human race would be all Noah's tribe in one place. 
Secondly, if someone else who never opposed Noah(AS) or who lived in some distant land, then what justice would it be to drown him and his family because someone in a far far land opposed Allah's prophet?  Behold Allah is most Just and Merciful. 
So even if it is a local flood it can destroy all of humanity except for Noah(AS) and his followers.  It is proven that mankind came from one man and woman so it will be a first tribe or a village of humans which contains all the population of mankind. 

A:

Many scholar of tafsir including Ibn Katheer based on few evidences in Quran suggests that the flood was global
For example in (Al-Sua'araa 119-120)

And We saved him and those with him in the laden ship, Then We drowned the rest (disbelievers) thereafter.  

And in Surrat Al-Saffaat says clearly that all humankind today are from prophet Noah

And, his progeny, them We made the survivors (i.e. Shem, Ham and Japheth)

After few ayas in the same context Allah says:

Then We drowned the others (disbelievers and polytheists). 

Also this agrees with prophet Noah' duaa

And Nûh (Noah) said: "My Lord!  Leave not one of the disbelievers on the earth! 

I do not understand what you mean by "If you consider that Earth was considered flat at that time", but anyways the earth was not flat at this time.