The safest way to apply an OS X update is to download Apple's Combo Update, which includes all updates since that major version appeared. But Leopard Combo Updates have the annoying characteristic of requiring a very long double start-up -- during which the computer may even hang. The whole process can be both time-consuming and nerve-wracking.
Luckily, the solution is simple: Don't update from your boot volume.
On my Mac, I always have at least three working copies of OS X:
1. My regular boot volume, named "OSX".
2. A "Test" volume for trying out software, updates, and fixes before applying them to my boot volume. As necessary, I update this by copying from my boot volume with SuperDuper.
3. A "Maintenance" volume for performing repairs to the boot volume. I update this one too with SuperDuper -- but it usually lags behind the boot volume by an update or two, so I can be sure it's available to save me from any problems an update might introduce.
When Apple announces an update to Leopard, I download the Combo Update from the Apple site. Then I boot into "Maintenance" and apply the update to my boot volume from there.
The result is that the update is complete within a few minutes and after only a quick, single start-up. Try it, you'll like it!