How should calibration points be distributed?
For that I have some guidelines, which I'd like to share. Even though some of these might not be valid for certain calibration software, for typical cases, they hold:

1) The entire pattern should be visible in all sequences.
2) At least 1/4th of the image should be occupied by the pattern.
3) Preferably, the lighting should be uniform everywhere on the pattern. 
(As little shadows as possible)
4) The light should reflect from the pattern to the camera (as much as possible). 
Thus, objects made up of metal are not suggested.
5) There should be minimal blur. If focus/depth-of-field is an issue, 
use a smaller plate or less tilts.
6) If you can't fix the camera, it shouldn't move at all. 
For extrinsic calibration, moving the camera after calibrating will ruin the entire 
calibration. Be careful about this as even small shakes or movements distort the accuracy.
7) Don't pre-process the calibration images. 
Even if you do very smart things, you might perturb the accuracy.
8) Ideally, have 15-50 images fitting the above criterion. 
This should give you 450-1500 points to optimize in total.
9) If you are printing the pattern on a piece of paper, then make sure that 
contrast between black-white squares is significant and no strange shape is appears on the paper. 
10) Don't bend the calibration pattern. Make sure that it is as rigid (and planar) as possible
11) If you are printing on an A4 paper, make sure you have some white space around the pattern, 
remember you will want to hold it somehow.
12) If you have distortion, use small circles, they are less affected from distortion. 
If you have low resolution but less distortion use larger circles. 
13) Start with low tilts and fronto-parallel images. 
Move to the tilts and rotations in all axes, gradually, covering the entire visible space.
If you have bias in the space coverage or distribution of points, 
then it means that some regions of the space will be better calibrated.
Keep this as equal as possible. Some variation can be tolerated.


I hope these help.