Is it common for slow cookers to heat unevenly? I have a CrockPot brand slow cooker that is less than one year old.  I have recently realized that it heats rather unevenly, being considerably cooler on the side near the controls than on the opposite side.  For example, when I cook a batch of chili, I can see it bubbling bubbling near the warm-side wall, but not on the opposite side.  If I cook dumplings in my chili then those on the warm side are done in about the amount of time I expect, but those on the cool side are still decidedly undone at that time. For what it's worth, I usually use the "low" heat setting, but I think similar behavior occurs on "high".

Questions: Is this kind of uneven heating typical for slow cookers?  Does it indicate that mine is broken?  Do you have any advice about how to deal with it, beyond stirring and/or occasionally turning the crock within the heating unit?
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.