In a bi-weekly payroll cycle, there are only ever 26 pay dates, correct? In a bi-weekly payroll cycle, there are only ever 26 pay dates, correct?  It never jumps to 27 or falls to 25?  

I'm asking this question in a leap year, and I know that calculating the first pay date has to do with selecting a day of the week to run payroll on, and then selecting the first occurrence of that day in the year.
You mean 26 pay dates per year, right?

Then no, because a year is 365 days long and a 26 biweeks are $26 \cdot 14 = 364$ days long. Therefore any year that starts with a Friday (which is usually a pay date) should have 27 pay dates. However if Jan 1 is a holiday (depends on where you live), the paydate is probably moved to Dec 31 so the preceding year would have 27 pay dates.