You should only connect to the database as user SDE if you are doing an upgrade
(at which time, a whole lot more than SELECT ANY TABLE will be necessary).
SELECT ANY TABLE is NOT necessary for the ArcSDE application server to function.
The ArcSDE data dictionary tables are hidden when you connect through ArcGIS
(intentionally, since you shouldn't ever be changing them), but access to them
is necessary for ArcSDE to function.
You should also see all the other tables to which you have been granted at least
SELECT access. In addition, you will see aa list of all featuredatasets, since
these are not database objects and there is no way to determine access without
walking the member list and testing the permissions of all the tables of all the
member featureclasses (very slow).
Nothing you have described matches the "wrong tables" in the title.
- V