Will changing pedals every week lead to long-term problems?
Changing pedals every week should not cause problems long term if correctly done.

Here are the possible types of issues changing pedals could create.


Cross threading - this includes normal cross threading and getting the wrong pedal on the wrong side.
Thread wear - from installing and uninstalling - cranks are aluminum (usually) and pedals are steel (usually). Wear would be on the softer material - usually aluminum.
Over / under tightening - over tightening damages threads in the softer material, under tightening risks the pedal working it's way out tearing out the last few threads in a worst case scenario.


All that being said correctly uninstalling and installing pedals should not cause long term problems.