In the past I worked on a project where as an ''inquisitor'' of some sort you had to hunt down the 72 demons from here (
http://en.wikipedia.org/wiki/Lesser_Key_of_Solomon) so I thought about all of this quite a lot, segregating demons into categories (aka the 7 sins) and then creating subcategories for each one of them. Each one had a specialty, difficulty depended on the demon's rank, some were friendly, manipulative, all that stuff. And nope, I'm really not a cultist.
Anyway, I think that no matter how much you try each ''minor'' sin will be somehow linked to an existing major sin, so I'd recommend just branching out from the 7, having minor ones linked but not based on them. In any case, here are some aspects that could be considered minor sins:
- Manipulation - the need to control and know everything about everyone to an unnatural extent. Stalkers, secret services, all that stuff.
- ''Leeching'' or Freeloading - the need for others to do everything for you. Not just being lazy, but purposefully making others do your chores.
- Squander or being wasteful - losing things due to negligence and inaction, definitely linked to sloth but probably more severe than spending the day watching YouTube,

Also, purposefully destroying things just so that others won't get them when you don't need them. Scorched earth mentality.
- Absolution - the refusal to change one's mind even when presented with solid evidence. Also, racism (all X are evil, no matter who they are), etc.
- Depravation - the goriest and nastiest stuff goes there, simply for the shock value or some perverse ideal. Calculated and cold, unlike wrath - probably more linked to lust as it's linked with the worst kinds of crimes. Fate/Zero had an interesting character, aka the Mage that is a perfect example of just how depraved one can be without being furious while thinking that all the actions make perfect sense.
- Irresponsibility - drunk driving or fighting monsters under drugs? Same thing, putting others in danger because of completely unnecessary and avoidable actions, at least most of the time.
Anyway, been a while since I thought about that stuff. If I'll come up with more I'll post them here.
And yeah @DragonVine, if you look at some documents and stuff like that Pride is usually the most severe sin in most religious texts simply because it's the one from which most sins are born. Some would be a stretch, but almost all can be linked back, no matter how silly the connection looks. Also, in Christianity, each of the Deadly sins has a ''patron demon'', Pride having the most powerful one - Lucifer, or Satan. Few have heard of the demons that are linked to Gluttony or Sloth.
EDIT: Also, a little tip - if you're looking for dungeons / quests based around the deadly sins having a look at those 72 demons may be worthwhile, some of them have awesome back stories that are just perfect for a quest to be centered around them - ex: ''Ose – he brings insanity to any person the conjurer wishes, making him/her believe that he/she is the creature or thing the magician desired, or makes that person think he is a king and wearing a crown, or a Pope. ''