When editing a python file eclim will default to validating the file when it is written. Any errors will be added to the current window's location list (:help location-list) and their corresponding line number noted via Vim's sign functionality.
If you don't want python files validated when saving them, you can set the g:EclimPythonValidate variable described in the configuration section below.
Regardless of whether you have validation enabled upon saving or not, the command :Validate is available to manual validate the file.
g:EclimPythonValidate (Default 1) - If set to 0, disables python validation when saving the file.
When enabled, syntastic is disabled so that eclim and syntastic don't step on each other. If you'd like to use syntastic over eclim for validation, then simply disable eclim's validation.
If you'd like to disable eclim's source code validation for all languages, eclim provides a global variable for that as well:
let g:EclimFileTypeValidate = 0
g:EclimValidateSortResults (Default: 'occurrence') - If set to 'severity', the validation results will be sorted by severity (errors > warnings > info > etc.)