Sync with Omnifocus on Mac adds completed tasks..
 

I'm not sure what happened but for some reason, on the iPhone app it shows all completed single action tasks that I have completed. How do I remove them since they are completed? Omnifocus on my Mac does not do the same behavior.

You've set your view settings to show completed actions — they are also present on your Mac, just not being shown. Tap the little "eyeball" icon at the bottom of the screen to bring up the View Settings, then make sure you don't have "All" checked. There is a separate View Settings page for both Projects and Contexts. Common practice is to show Remaining actions for the Projects view (where you typically do planning), and show Available (or Next Actions) in Contexts view (where you typically choose tasks to perform).

for some reason I can't tap the eyeball, it is grayed out. How can I change this on the Mac? Will that setting cross over to the iPhone? I changed my sync settings to MobileMe if that means anything?

No, this is the equivalent of the View->Availability Filter on the Mac, and does not sync. Go to the Projects display (tap Projects on the home screen of the app) and you should be able to tap the eyeball. Similarly, go to the Contexts display to enable the settings for Contexts. It needs to know which sort of display you are configuring, and does so by looking at the current display.

this settings will only change the view for contexts and projects correct? what about the Inbox then?

Ah, now the setting for the Inbox does sync from the Mac. In the preferences on the Mac, in the Data section, there's a checkbox for Clean up completed Inbox items. If that is checked and the Mac and iPhone are synced, the iPhone should hide completed items in the Inbox. General practice is that one moves actions off into projects before doing them (unless they are trivial), but as you've seen, it is certainly possible to mark Inbox actions as completed without doing so.

the completed items were removed from the inbox on my iphone after I tweaked some things but am still unsure how the cleanup works..

Clean Up does a number of things, including:
[LIST][*]Removes items which do not match the current view settings from the view[*]Moves items out of the Inbox to their destination, if project and context match the conditions specified in the Data preferences[*]Refreshes the view[/LIST]In no case does Clean Up actually remove items from the database, but it may hide them from sight. When you complete an action or project, it is simply marked complete, and although it may disappear from sight, it is not deleted.

Clean Up is done when you press cmd-K or the Clean Up toolbar button, use Edit→Clean Up, or switch views.