The real problem I see here is that you're not just innocently looking through his phone. You're trying to catch him doing something. Once you've got that mentality, it's time to put the technology down and have a real c-o-n-v-e-r-s-a-t-i-o-n about your insecurity, loss of trust, why its happening, and what needs to be fixed and how. If it gets to the point that you feel you need to snoop, there are bigger problems in the relationship, and snooping doesn't fix them.
And don't for a minute think that looking at his phone or his facebook regularly is a sure sign that nothing is happening. If an untrustworthy person wants to do something without their sig other knowing, they will find a way to do it. One can have multiple secret/private social networking profiles, multiple (secret) phones, they can create a whole new persona if they want to and are good enough at keeping it under wraps. So if you're already dealing with someone you don't trust, looking as his phone will do nothing. The only way to rectify the issue (that being trust, or lack thereof) is to deal with the issue itself.
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