Is it common for slow cookers to heat unevenly?
It is not typical for the heating to be that uneven in a slow cooker, it sounds like it is broken. If it's less than a year old send it back and get a warranty replacement! 

If it's not under warranty if it was me I'd take it apart and fix it if I could, they aren't very complicated. I'd either fix it or replace it rather than try to use it because one of the big benefits of a slow cooker is to be able to leave it unattended. You could stir things occasionally, but slow cooker temperatures are very low and you'll lose a lot of heat each time so it's not recommended.