Thanks for your reponse.
It happened no matter how simple or complex my application. I have now made the problem go away. I'll tell you what I did.
First I re-started the computer. Then I tried to build a very simple application and it worked. But when I tried again, it failed with Error 10. So I restarted labview and it stll failed with error 10. The only way I could get it to build the app was to restart the computer and then it would only build it the once.
Then I started looking at some of the VI's that are part of the app builder and I got a little suspicious because some seemed to be linked to the LabVIEW 8.0 folder, not the 8.2. I had LabVIEW version 7.0, 7.1, 8.0 and 8.2 on my computer.
I removed all but version 8.2 and now the build works every time. So I think somehow the app builder VI's got crosslinked between versions after the first time I built and app in 8.2. I don't know how this happened since I actually rarely, if ever, have tried to use the app builder on my mac. I can't imagine a case in which I had Labview 8.0 and 8.2 open at the same time and built an application with one of them.