System Tables.  The mysql.proc.comment column definition changed between MySQL 5.1 and 5.5. After downgrading from 5.5 to 5.1, this table is seen as corrupt and in need of repair. Running mysql_upgrade from the version of MySQL to which you downgraded (as documented in the downgrade procedures) reverts the mysql.proc.comment column definition.

InnoDB.  MySQL 5.5 uses InnoDB Plugin as the built-in version of InnoDB. MySQL 5.1 includes InnoDB Plugin as of 5.1.38, but as an option that must be enabled explicitly. See the Release Notes for MySQL 5.1.38.

Tables partitioned by [LINEAR] KEY.  MySQL 5.5 implements new functions used to calculate row placement for tables partitioned by KEY and LINEAR KEY. Tables that were created using KEY or LINEAR KEY partitioning in MySQL 5.5 cannot be used by a MySQL 5.1 server. In MySQL 5.5.31 and later, you can downgrade such tables with ALTER TABLE ... PARTITION BY ALGORITHM=1 [LINEAR] KEY (...) to make them compatible with MySQL 5.1.