I've noticed that but not with daily or weekly tasks. They simply can't be added after you complete enough tasks in one day.
However the tasks that are under available tasks bar still can be added and completed. I call them tutorial tasks as they are the same you get automatically through tutorial progression. They are easy and give you little xp and coin.
So when you complete such a task you get a message in the middle of your screen and the xp bar appears in the top right corner. However, the bar doesn't show any progress. In my case it's always empty meaning it's all grey and no blue progression is ever shown. I did several such tasks and it stays the same.
My guess was that after reaching the limit of daily tasks you can't get any other xp and coins as a part of a design rather than a bug. Or maybe these tutorial tasks never give you xp and coins unless they are assigned to you by tutorial system? Either way it would be better if you couldn't activate them via tasks menu at all.