Whenever an operating system is upgraded, there are always some applications or system services that will behave oddly. In some instances, applications will not display properly, or the system will slow down, have unexpected behavior, or show interface oddities.
These problems seem, for the most part, to be from two possibilities: corruption in temporary files such as preferences and caches, and incompatible third-party software.
Caches and temporary files
When applications are run, they store temporary files and settings in caches and preferences, which are then quickly accessed later. If these files are corrupted, then the program may not be able to refresh them and will continue to load and manage the corrupt data, resulting in odd behaviors. Tackling problems with these files is fairly simple to do. The best way is to first use a utility to clean out system caches and temporary items. Such a utility might be MacCleanse, OnyX, MainMenu, or any other system cleaning utility. You can search for these at VersionTracker or by checking the MacFixIt Utilities topic.
Be sure to check with the utilities' developer to ensure that it is compatible with your operating system version. This is particularly important for newly released OS software, since running older utilities may cause more problems. Unfortunately this can take a little time, but given the number of reputable OS X cleaning programs out there, one is bound to be updated and working for the latest OS very soon after its release.
In addition to caches, you can find the preference files for various programs that are exhibiting problems and remove them. This will reset customized settings for the program, but may result in proper behavior again. Preference files are usually in the form: domain.company.program.plist, such as "com.apple.Mail.plist" for Mail, or "org.mozilla.Firefox.plist" for Firefox, and are usually stored in the /username/Library/Preferences/ folder (though some are in the /Macintosh HD/Library/Preferences/ folder).
Removing a preference file for a program will not harm an application, and relaunching the program will replace the file with a properly structured and formatted one. At most, you may have to enter registration information again, or apply customized settings back to the program after relaunch.
If you have run a variety of third-party applications, especially those that add system functionality such as firewalls, system monitors, or any item that runs in the background or in the system menus, you may run into problems if you continue to use them after updating your operating system and they are not compatible with the new environment. For instance, one Apple discussion poster found that a program "iClock" was causing menu items to double up until he updated to a release that was compatible with Snow Leopard.
If you have third-party utilities or other system enhancements running and are experiencing problems, try disabling them all and clearing the system caches (mentioned above) to see if problems go away. Then, update the utilities accordingly, and only enable them if they've been updated to run on your new system software.
You can test if the problem is account specific by creating a new temporary user account to run for a while, and see if the problems persist there. If not, then the problem is more than likely in your old account's Library folder. Additionally, you can turn off third-party kernel extensions by booting into Safe Mode (hold shift at start-up), which will test for problems with extensions.