After launching SP1 for PerformancePoint Server 2007, on many internet forums about PPS, I’ve found many posts describing errors while installing SP1.
For example, one of them described problems with planning applications, which disappeared in Business Modeler after upgrading Planning Server with SP1.

Installing SP1, specially for Planning Server, it is not only running SP1 installation files, but many other important steps.
So, if you omit some of them, you can receive different errors like this above.
If you are going to upgrade your PerformancePoint Server, I strongly recommend to review the following articles, before you start this procedure:

Detailed instructions on Microsoft Technet:

Updating PerformancePoint 2007 Planning Server with Service Pack 1

Updating PerformancePoint 2007 Monitoring Server with Service Pack 1

And if you need another step by step instruction with many screenshots included, read the following article:
http://performancepoint07.blogspot.com/2008/06/installing-performancepoint-planning.html