You have an application that works fine in SQL2005.
You need to move it to a server running SQL2008. To minimise your migration effort you run it in "SQL2005 compatibility mode" on your shiny new SQL2008 server.
Now the clincher for me is "Why would you choose to do this?"
The obvious answer is because you are not planning to do any testing. Well good luck with that one!
If you move from SQL2005 to SQL2008 you had better test that your application works Just Fine. Maybe there will be fewer things to fix if you stick with the old Compatibility Mode. But ... my view is, if you have to do all that testing anyway why not also change to the latest compatibility mode? then you know that your application works fine with that mode, and you can then take advantage of any new features you choose to, and you've future-proofed yourself for a good while longer too ...
Do bear in mind that some behaviour changes apply regardless of the compat level. I don't have a handy example, but I do recall from when I was upgrading a DB to 2005 some queries worked on SQL 2000 but not on 2005, even in compat mode 80.