Whenever I load my txt, it doesn't seem to be drawing tiles in the proper locations. For example (in my case) tile 4 is where tile 2 should be and vice versa. What am I doing wrong?

// The map loading function

void LoadMap(const string& filename) 
{    
  ifstream file; 
  file.open(("data/"+filename+".txt").c_str(), ios::in); 
  for(x = 0; x < MAP_W; x++) 
    for(y = 0; y < MAP_H; y++)
      file >> mMapArray[x][y];
  file.close();
}

// Drawing the map

  for(x = 0; x < MAP_W; x++) 
    for(y = 0; y < MAP_H; y++)
      mTile[mMapArray[x][y]]->Draw(...)

This is how my txt looks.

6 2 2 2 2 2 2 2 2 7 
4 1 1 1 1 1 1 1 1 5 
4 1 1 1 1 1 1 1 1 5 
4 1 1 1 1 1 1 1 1 5 
4 1 1 1 1 1 1 1 1 5 
4 1 1 1 1 1 1 1 1 5 
4 1 1 1 1 1 1 1 1 5 
4 1 1 1 1 1 1 1 1 5 
4 1 1 1 1 1 1 1 1 5 
8 3 3 3 3 3 3 3 3 9

And this is how it's displaying it.

6 4 4 4 4 4 4 4 4 8
2 1 1 1 1 1 1 1 1 2 
2 1 1 1 1 1 1 1 1 2 
2 1 1 1 1 1 1 1 1 2 
2 1 1 1 1 1 1 1 1 2 
2 1 1 1 1 1 1 1 1 2 
2 1 1 1 1 1 1 1 1 2 
2 1 1 1 1 1 1 1 1 2 
2 1 1 1 1 1 1 1 1 2 
7 5 5 5 5 5 5 5 5 9

Also it's generally better to store maps in (y,x) since you'll naturally want to access them rows at a time.

One thing I notice is :

  for(x = 0; x < MAP_W; x++) 
    for(y = 0; y < MAP_H; y++)
      mTile[mMapArray[x][y]->Draw(...)

Probably a typo , but mMapArray probably isn't a pointer and the data not pointed to by it doesn't have a member named Draw does it? (Missing square bracket)
Shouldn't it be :
(mTile[ mMapArray[x][y] ])->Draw(...)

Global variables can screw things up when you go to modify your program. I try to make all my functions autonomous by passing them all the information they need or making them capable of getting it themselves.

In LoadMap the line :
file >> mMapArray[x][y];

What data type is mMapArray? Is it integer?

The extraction operator '>>' can be a little tricky. Check out 'manipulators' at this page on operator>>

Did Jonatan and Matthew's advice fix all your problems?

Is this line psuedo-code? BITMAP objects don't have any methods named Draw.
mTile[mMapArray[x][y]]->Draw(...)

Is mTile a pointer to a bitmap pointer? (BITMAP**)
What is your drawing code?

You could change your class into 3D instead of 2D , just add a variable for layer or depth or height and resize everything. You would have to rewrite your operators() then but that wouldn't be too hard.

After that , just load one layer from one text map at a time.

bool LoadMapLevel(const string& filename , int maplevel) {
  // maplevel from 0 to number of levels - 1 , with 0 being ground level or lowest
  ifstream file;
  file.open(("data/"+filename+".txt").c_str() , ios::in);
  if (!(file.good())) {return false;}
  for (int Row = 0 ; Row < MAP_H ; Row++) {
    for (int Col = 0 ; Col < MAP_W ; Col++) {
      file >> mMapArray[( (maplevel*(MaxNumRow*MaxNumCol) + Row*MaxNumCol + Col)];
      if (file.eof()) {return false;}
    }
  }
  return true;
}

I would make LoadMapLevel a member of a wrapper class for Array3D and I would make Array3D know all of its bounds , not just the number of columns.

Store each layer of the map in a different text file.

Put the layers one after each other, and put the loading inside a for(l = 0; l < LAYERS_NUMBER; l++) { /* loading here */ } ?