What effect does the Space Shuttle have on the Shuttle Carrier 747
@fooot beat me to it in the comments but the linked podcast answers all your questions

The shuttle effected lots of factors of flight, in quick summary (from the info in the podcast) the whole assembly was: 


...aerodynamics not neutral as is answered in this question
...Speed limited due to the braces that held the shuttle on
...VFR only due to the fact that impacting rain could cause water build up issues in the heat shield tiles 
...Altitude limited 
...Bank angle limited 
...Quite short range by default
...Required the orbiter to be empty (although hypergolic fuels were left onboard. All payloads had to be removed if the orbiter was returning something. 
...Required rib re-enforcements where the braces were mounted 
...Was quite noisy due to the brackets used to hold the orbiter on