Sorry, old topic, but I thought I should mention for other people who read this topic; You are limited on more than just berries and Umbreon/Espeon.
-The tide in Shoal Cave doesn't change, meaning you can't get shoal salt/shells and you have a chance of not being able to catch Snorunt.
-No berries
-No Espeon/Umbreon
-The Lotto Ticket in Dewford NEVER changes
-Eggs not being created (Possible, but not always)
-And a chance that because the cartridge hasn't had power for a long time (Say you don't play it for a year and the battery has been dead for longer), your save can be deleted and/or corrupted.