I have a student that when I print her report card, it shows last years first quarter and final grades, as well as this years second and third quarter grades. She transferred back to our school during second quarter but we input in the "transfer grades" from last year and now it is showing on this years report card.
If you use an Object Report template for your report card, it will display all grades unless you make some adjustments to the Transcript Object. You can set credit types, grade levels, and/or tell it to pull from the "Current School Only." If using "Current School Only," you must make sure to enter transfer grades with your school set to District Office so that the SchoolID on the grades is 0, which will prevent them from showing up on the report card if you run it at the student's home building.
Someone will also need to use DDA to change the SchoolID on all grades to 0 at the end of the year after all grades are stored to prevent previous years' grades from showing up on report cards.