Hector,
The JS API is backward compatible so you should be able to use the latet 3.3 with a 9.3.1 server. The only caveat is that you cannot use JS API features that aren't supported by the release of ArcGIS Server you're using. For instance, you would not be able to do any editing against your services or time aware layers etc. If you're just displaying and querying, you should be good to go.
Regards
Anthony