We use separate accounts for additional safety. The admin accounts pretty much only get used from our workstations, our regular accounts could get used anywhere and are much more likely to encounter something malicious (for instance, keyloggers at an internet cafe). With the admin accounts we don't use most of the services, we forward the mail and they're just for Admin console work. That's more of a matter of logistics - I already have an institutional account and a personal gmail account, there's no way I want to deal with a second institutional account with its own set of docs and all the other stuff.
The third-party app access doesn't particularly worry me, that type of thing has been around for a while now and it seems like a pretty robust system. It concerns me in the same way that accidentally sharing something with the wrong person concerns me - possible, but unlikely to happen if you're careful.
One thing we did do is add some read-only admin rights to our personal accounts so it's not always necessary to switch over just to look up someone's status or find the support contact info.
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Adam Nave, CISSP
Linux/Unix Systems Administrator
Macalester College