If I have no errors when entering my 1099-SA information, how do I advance to the next step when the program keeps telling me to fix errors?

I assume there is an error reported on the 1099-SA?

Not knowing what the error message is, the simplest thing to do is to delete and re-enter the 1099-SA. 

You can delete the 1099-SA by either on the "Here's what we have so far" screen where there is a table showing 1099-SAs already started, or you can do the following:

*** Desktop***

1. go to View (at the top), choose Forms, and select the desired form. Note the Delete Form button at the bottom of the screen.

*** Online ***

1. go to Tax Tools (on the left), and navigate to Tools->Delete a form

2. delete form(s) 1099-SA (if one), 8889-T, and 8889-S (if one) 

Now restart the HSA interview, skipping past the 1099-SA section when you come to it.