Because I breed fancy rats of sooo many different colours, pattern and coat types, I just know who is related to who and can remember it all. I have many different projects going on and I cull babies that don't look like the typical look for each project, so I can tell by looking at a rat where it has come from etc. for example all the dalmation rats have spots in different places and I remember them all. If the silk rats have non silk babies, I cull them so I don't mix up the lines with my other rats of similar colour and marking.
If I was only breeding for reptile food I probably wouldn't bother with all that, but I need to know all the ins and outs of a duck's backside and I refuse to write anything down lol.
In terms of remembering different mothering traits though- basically if it is alive, it is a good mother or hasn't had a litter yet. I don't keep any rats that get sick, bite, or have any other problems. Therefore I can assume everything I am looking at is super awesome, until it gives me a reason to say bye bye.
There was one exception to this rule with my silk rats. I only got 2 females and both were bitey mothers. If I culled them I would have no more silks! Within 2 generations I have silk mums that don't bite me ever and so I am able to cull any that pop up that are biting now.