You could have very well damaged the home button cable during the repair. Even a microtear in the cable can cause the home button to malfunction.
Also keep in mind that home buttons have a rubber gasket around them. This gasket is very similar to other gaskets (ie engine gasket) that sometimes need to be replaced during the repair due to general wear and tear.
If the home button does not click properly, try readjusting it or replacing the gasket. If your home button in fact did get damaged during the repair, replacing it is simple, but you will not have any touch id afterwards because home buttons are married to the motherboard inside your phone. If they are not able to talk to eachother anymore, then you will not have the touchid option available.