What could cause contact syncing errors on iPhone? I deleted a contact about two years ago and it now appears under another person's contact. I have deleted all numbers for the contact I no longer need, but when I sync to computer Gmail the number appears with a different name on the number. 

For example:
"Brad's" number is (743) 222-2222 but I deleted this contact out of my iPhone. However it now appears under "Ted's" name.

So now "Ted's" number is listed as (743) 222-2222, and Ted's real number is gone - "Brad's" number (which was deleted) actually replaced "Ted's" real number?

Any ideas of why this would happen? It has done it with three other contacts as well.
From your question, I think your setup involves syncing contacts with Google, a computer (Mac?), and an iPhone. Syncing with Google has been a pile of poo since Mountain Lion. For me, it kept duplicating contacts, bringing back deleted ones, and as you mentioned, swapping the contact information between contacts. 

Since neither Apple nor Google seem to care about fixing it, my solution is to use iCloud to sync contacts between the Mac and iPhone. (This seems to be Apple's preferred method, so it's the one in which bugs will likely be fixed the fastest.) I periodically upload a vCard of my contacts to Google. This is a lot less work than hunting down all the contacts that syncing with Google messes up.