You've selected a specific kpi_date, right? Even your working expression could be simplified.
sum({<KPI={'NEW REGISTRATIONS'}>} registration_count)
The only thing that really matters is that I removed the kpi_date check. You already have it selected, so there's no need to use set analysis to pick what you selected. On top of that I removed the $ because it isn't necessary, and I put "NEW REGISTRATIONS" in single quotes. Single quotes for literals, double quotes for search strings. Now if you search for "NEW REGISTRATIONS" it will find 'NEW REGISTRATIONS', so they are functionally equivalent, and any performance difference is probably measured in picoseconds or something, but there's still no reason to search.
You have a couple problems with the second expression. First, no reason to getfieldselections. You can just refer to kpi_date directly. In fact, I THINK the getfieldselections might return the text version of the date, in which case you'd fail to subtract 1, return null, and not find it. But if you just use kpi_date, you kind of have the opposite problem. Not it takes it as a number and subtracts 1 from it. That would be fine except for a QlikView shortcoming - QlikView compares the text equivalent of your date to the text equivalent of your expression. So it would end up comparing text like '05/06/11' to 40651 or whatever, and find that they don't match. So when using dates in set analysis, you have to make sure they remain formatted as dates, and in the same format as the field you're comparing them to. I suspect this would do the trick:
sum({<KPI={'NEW REGISTRATIONS'},kpi_date={'$(=date(kpi_date - 1))'}>} registration_count)
If not, perhaps kpi_date isn't in your default date format, and you'll need to add a formatting string to the date() function in there. Or maybe I have a syntax or other error.
