<p>Is there any technology out there that will allow you to do side-by-side updates of production schemas?</p>

<p>The goal is to have zero down time when applying updates to a schema in production.
Weblogic 10 has a similar feature for their Java EE apps where by you deploy the new version of the app and new connections go to the new app, while the existing connections continue to the old app.  When all the old connections complete/timeout, the old app is retired and the new app continues on...zero down time.  </p>

<p>Is there something similar in Oracle?</p>

Yes. There is online redefinition package.
DBMS_Redefinition
But I doubt this will give you zero downtime, this doesn't account for every possible change to a schema. This lets you do some table changes. I think you need to define zero and how extensive the changes you want to make. Usually if you change the database, you have to change your client as well. If you changed your database, how would the client switch automatically from the old proc signature to the new proc signature - Instantaneously?
Databases don't work like apps. There either is a FK from tableA to tableB or there isn't... it can't not be there for current connection and exist only for new connection in the same manner as your application can. Databases just aren't the same.
That being said, there is rumor that Oracle is working on package versioning... so you could connect to a specific version of a package to make such a migration simpler. But again... that would work for packages, DBMS_redef would work for tables... but that's not the sum total of your database.