Great gift for your Mom. I'm sure she will be thrilled with it. I wouldn't worry too much about it either way because should it have any issues I'm sure you have to January to exchange/return it. Well, that is assuming you bought it within the last month or so as most stores allow Christmas returns until January.
There's no way of telling, is there?. If your mom reads a lot of black text on white, and the screen has that yellowish unevenness, then she may notice. If she's just watching videos I doubt she'll care.
Sorry but I don't think you can discern screen quality by the serial number. I also don't think whole batches of iPads are defective - I could be wrong but I think the majority of tablets are fine and only a fraction are having issues