Yes you should be concerned as that isn't normal, but it's not the fault of the update, although the update may have triggered something already wrong with your system.
Open the Activity Monitor in the Utilities folder. Select All Processes from the Processes drop down menu and click twice on the CPU column to display in descending order. Look for a process using a large amount of CPU time. Note what that process is then force quit it.
Now, you need to do the following:
Repairing the Hard Drive and Permissions
Boot from your OS X Installer disc. After the installer loads select your language and click on the Continue button. When the menu bar appears select Disk Utility from the Installer menu (Utilities menu for Tiger and Leopard.) After DU loads select your hard drive entry (mfgr.'s ID and drive size) from the the left side list. In the DU status area you will see an entry for the S.M.A.R.T. status of the hard drive. If it does not say "Verified" then the hard drive is failing or failed. (SMART status is not reported on external Firewire or USB drives.) If the drive is "Verified" then select your OS X volume from the list on the left (sub-entry below the drive entry,) click on the First Aid tab, then click on the Repair Disk button. If DU reports any errors that have been fixed, then re-run Repair Disk until no errors are reported. If no errors are reported click on the Repair Permissions button. Wait until the operation completes, then quit DU and return to the installer. Now restart normally.
If DU reports errors it cannot fix, then you will need Disk Warrior (4.0 for Tiger, and 4.1 for Leopard) and/or TechTool Pro (4.6.1 for Leopard) to repair the drive. If you don't have either of them or if neither of them can fix the drive, then you will need to reformat the drive and reinstall OS X.
After completing the repairs quit DU. Now download the
10.5.6 Combo Updater and reinstall the update.