There are many new software and optical tools out there for polar alignment - and I think people are comparing accuracy and ease of use. When you are down in the arc-minute regime - the error will hardly matter since drift in RA and dec. will always be present to some extent due to refraction. It is explained pretty well here and in associated pages:
It makes sense to get the mount as aligned as possible in azimuth - but for altitude it will depend on your latitude and the star's alt/az.
So when people say they are 1' off in altitude - is that relative to the geometric pole? What convention are people normally using?
This is mostly an academic issue because I don't think any particular altitude setting for the polar axis will work in general. But it's important to know what the reference point is when measuring polar alignment.