An example of the single parent vs couple parent where one person take on the mental load that I think is particularly common and while minor, can be extraordinarily irritating:
Children are small and need constant care and supervision. Man wants to play football with mates after work. Man calls wife and tells her he is going to play football. Man is then confused when wife is very angry and annoyed.
Except, man did not think about the fact that the family had a lot going on that evening. Man had no idea (because he just doesn't register any of this stuff) that tomorrow is the first day of school for little Johnny who is feeling apprehensive and therefore needs a little extra support. This is tricky because dinner still has to be made, the baby still has to be fed etc. Also, because woman has been at work all day, she also has a bunch of additional tasks that need completing. Also, woman knows that when man goes to football, he goes for drinks after. This means he is likely to be hungover in the morning. Which is tricky becuase Johnny has first day at school, things are likely to be a bit stressful and she' dlike him to actually take part in all this.
Such a minor thing and yet so classic.
My DH recently booked a weekend away. No problem with that and he asked me and I said sure, no problem if we don't have anything else on. My Dh did not actually check the diary (apparenrly "if we don't have anything else on" in his head was "I have checked the diary and we don't have anything else on" ) so he did not notice that we actually do have something very important on that weekend. He seemed to think I just hold all these important dates in my head, even when they are months ahead of time.
My DH is not a dick so once that became clear, he apologised and has spent a lot of time and effort reorganising his weekend away. But it took time to get to this point. My other favourite complete-lack-of-thinking habit he used to have would be, for example, saying to me,
"I'd like to do x thing on Saturday morning. We have nothing in the diary for that time - 12:00." [pats himself on back for looking in diary]
Me: But DD has dance class from 10-12:00 and DS has his football match from 10:30. How are you planning to get whichever one of them YOU are with back to ME in time for YOU to be at xx by 12:00?
that is an example of the silly small things that are part of the mental load that are nonetheless ENDLESS, where it is more problematic and frustrating in a relationship than when you are single because it just doesn' thappen when single.