This post has been in my drafts for quite a long time. I noticed it today and it was almost ready to get published. So, with very minor changes, I am posting it today. Couple of months ago, I had setup 10g OEM in my laptop to try and explore it, and below explained were some challenges I had experienced. Hope they help...

(1)
Symptoms
- Oracle Enterprise Manager (null) - in the browser title
- Enterprise Manager is not able to connect to database instance - error message

OEM uses SYSMAN account to monitor a database.

Changing SYSMAN user's password is not a straight forward approach. We can straight away go ahead and change its password, but OEM can't recognize the new password. When OEM is deployed, at the time of dbconsole creation, SYSMAN's password gets captured in OEM's property file in encrypted format, and we have to fix that file as well when we decide to change SYSMAN password.

A googling of this issue helped with many sources...one I followed one is below

http://forums.oracle.com/forums/thread.jspa?threadID=368185

In the discussion happened in above link, it was suggested to change
$ORACLE_HOME/host_sid/sysman/config/emoms.properties file with new password information without encryption. However, after we restart the dbconsole, "emoms.properties" file gets recreated automatically with encryption enabled back.

(2)
dbconsole: java.lang.exception: no such metric

By now, with the above fix described in (1), OEM was able to connect to the database, but the metric information was still not available. Reason being was similar to SYSMAN issue - OEM was unable to connect to Database using DBSNMP user. So, just make sure you provide the correct login details for DBSNMP (unlock it, if locked and setup with new password in "Monitoring Configuration"). Below link from Don Burleson helps...

http://www.dba-oracle.com/sf_error_dbconsole_java_lang_exception_no_such_metric.htm

- Karteek