I mean buying one that someone else leased. Looking at one at a dealership that was previously leased

Would be just like being a used car I guess, haven't ever had that experience.

My concern is that Ive heard about people beating the shit out of leased cars because they techincally arent theirs

That is indeed a true thing, just like buying a house. You have no idea what the other people did so all you can do is be very thorough.

Any tips for what I should look for, as far as mechanical without having to take it to another dealership or 3rd party source to be inspected , cosmetics are obvious of course.

Check all the fluids, tires to make sure the sidewalls aren't cracked and that there are no plugs. Smell under the carpets, check every electrical thing in the car to make sure it works. Get on your belly and look underneath the car for premature rust and stuff
If any of the body panels do not match perfectly do not even consider the car as it has been in an accident. Drive it to make sure it drives nicely, take your hands off the wheel and it if drifts to one side on an even plane you have a problem. If its a 4x4 or anything try engaging the 4x4.
Anything you can find that would lower the cars value bring up to them while you are seeing it and if you go to negotiate point these things out for sure. Also never buy a vehicle unless its in the day when you can see everything.

Hope this helps.

tyvm, ill keep it all in mind

This is the car that i`ll be getting, just applied for the loan

http://lansing.craigslist.org/cto/4254417845.html

Looks like a good enough deal as far as I can see.

defiantly, I was planning on getting the extended warranty regardless of where I got it so thats saving me money already and i havent been able to find one with that low of miles for that price and in that good of condition. The car is said to be flawless

Give it a week or two, if there is anything wrong it will show up within that time frame. And if it does, well who cares you have warranty.