I think this just means that certain methods called in the application are currently deprecated (i.e., in a future release they won't perform any action and may not even exist and hence raise an error). All the deprecation warnings shown there are warning you that in rails 2 they will be deprecated so as long as you are using rails < 2 (i.e., rails < edgerails) you won't have any problem.
Does the app actually start? Are you using the latest release version of rails (1.2.3)?