Upon completing the final 'review,' when entering 'signature' and date, just as I was clicking 'continue' I noticed that my wife's full name wasn't complete. How to fix?

Just click on the Personal Info tab.  It's the leftmost tab.

There isn't such a tab...  I have "My Info, Federal, State, Review, File" descending...  It was after the review (just prior to file) where you enter your full name and today's date....  looks like mis-clicked and the auto populate didn't populate my wife's full name.

Will that be an issue when filing?

The 'My Info' tab is the personal info tab that @Nazzlecrest was referring to.  Check to make sure that your spouse's full name and social security number are entered there correctly and if they are then you don't have anything to worry about.