This is quite odd I'd think...
I used to have a slackware distribution on my computer here at home (ext2 fs), and I read about loading bitmaps and they loaded fine; the tutorial files from nehe compiled fine, and ran smoothly. However, on my new distribution, Gentoo x86_64, reiser_fs, files are loaded incorrectly and slightly off. It's off slightly, not by much, as some fields are correct.

So, the question is, what is causing the same files, the same makefiles, to compile differently? (I know its not the filesystem because that fs ran fine at my school computer, which used slack/reiserfs)

If I ran the files I had on my old system from my backup, they run fine... they read the bitmap fine, etc... but If I recompile them on this system (The source from the tutorials, not stuff I wrote), it still reads information wrong. Heres an example of the information being read incorrectly after being compiled

Data at Offset: 171798691894
Width of Bitmap: 256
Height of Bitmap: 1572865
Error: number of Planes not 1!

Heres what it should be:
Data at Offset: 54
Width of Bitmap: 256
Height of Bitmap: 256
Bits per Pixel: 24
Size of the image data: 196608

Between your old and new systems are you compiling for 2 different processor architectures, where one is 32 and the other 64, or maybe PPC/Intel that have an endian change?

If you are recompiling from 32 to 64 bit, that's what the problem is. Longs go from 4 bytes to 8 bytes. If the program doesn't take that into account it may malfunction.