Oracle 10 to 11: charset issue
I had the same issue with a migration from 9i to 11g.  I decided that I did not want to take a chance that Oracle's character set conversion would do something I did not expect.  Managers don't care about character sets, they just want to know that the data was migrated without any problems. I kept the WE8MSWIN1252 character set and there were no problems.

However, if you had to have a UTF8 character set, and did not want to take any chances this is how I would do it.

Requirements:  a virtual machine in a test environment, to make the install and testing painless


start on the original 10g database in a test environment.
start a new instance of 11g on a virtual machine in a test environment with the old character set
import your data using a data pump or the old imp/exp.
test the web application to see what happens
if successful take a snapshot of the machine so you can revert to this 
establish what columns need to be larger. Usually these are LONG or possibly large VARCHAR2 fields
increase the size of the columns so conversion is not required
if you are able set up another Oracle 11 with the new character set and use the data pump to bring the data over.  If this is not feasible then do an export of your data and bring the virtual machine back to before the Oracle install.  Then install Oracle 11 g with the new character set and import the data. Ideally no conversion will occur if you have identified all the tables.
test the web application


Why go to all this extra work?  This solution breaks your project into two issues, the upgrade and the character set. Upgrading databases is not to be considered lightly. Many times it is not the upgrade that is the problem but peripheral problems like interactions with applications or other databases.  Custom PL/SQL code should have no problems but you never know.

If there is a problem people will be looking to you to explain how you were diligent and careful not how you saved a day or two.