As far as things like Java and Flash, the admins would need to ensure that when setting up a new computer that they install the latest client or update their image if they use an image to re-install windows. Obviously there are always going to be updates and if users don't have the permissions to perform the update you are always going to get this issue unless the admins created a scheduled task to perform these updates where required (this task would need to 'Run As' someone with the correct permissions).
IE preference/run once screen can be disable by entering the following registry key:
I am sure this is the fix but unable to test and confirm 100%
This would need to be applied to each computer, as this key is a 'LOCAL_MACHINE' change it will stop the pop up for all users.
Hope this helps.