Did you run utlrp.sql in the $ORACLE_HOME/rdbms/admin directory? That's one of the last steps in the upgrade and should recompile any objects that in reality are valid, but were left in an invalid status by the upgrade. If you've done so and the objects are still invalid, it will be necessary to investigate why.
I try to make it a habit to query prior to the upgrade for invalid objects and then compare what's invalid after the upgrade. That tells me whether the upgrade introduced new problems or whether the objects were already invalid beforehand.
Incidentally, I hate to disagree with my esteemed colleague, SantaMufasa, but in general you shouldn't be running the catalog scripts he recommends. Instead, it's better to stick closely to the installation instructions for the appropriate catalog script(s) to run. For example, the 10.2.0.3.0 patch set instructions tell you to run catupgrd.sql on each database affected by the upgrade, while the April, 2007 critical patch update says to run catcpu.sql. Most likely its harmless to recreate the entire catalog the way SantaMufasa says, but it's unnecessary and Oracle support won't like it if you have a problem and they find out you haven't followed their installation instructions.