Its the one you have been second guessing for years, and watching someone else scoop up the "deals".

The seller might have the best of intentions to living up to their end of the agreement but life throws unexpected curve balls.I would read your contract and see as mentioned what closing possession the seller has agreed to.If they want to change that agreement it is up to you to accept or not accept it but the sellers do not get a free ride for that and proper arrangements have to be made.Your agent you have to watch some of them.

Oxiclean or White Vinegar & Baking Soda.Grout Grime Buster 3000.... see this video:https://www.youtube.com/watch?

From watching ads on craigslist and stalking the listings on the website of the largest property owner/PM in the area for the past 8 months, I am wondering if there is an advantage to having one of few listings in the "off season" instead of having a listing when there are a bunch at the same time.

It can mean what you want it to mean.If you watch most fidelity commercials they mention self directed IRA frequently.

I'm not worried about the breed themselves (I'm a pit bull owner), but I don't want a dog biting one of the kids in the neighborhood and being sued (I feel like if they're responsible enough to have the requirements, they're responsible enough to watch their dogs around kids) Also, can I put in the rental agreement that they have to pay for any damages, including any injuries from the dog and carry additional insurance?

As a college student my monies would be very closely watched.

REI is a patience game and takes a lot of learning not just several months, it takes years.My advice to you is if you feel you are ready from reading enough books watching the market for a while and talking with real investors, then start small with a SFH learn what its is to be a landlord.  

My question is, what are the pitfalls or things to watch out for when negotiating and dealing with a house that still needs to be completed? 

Run away - most are considered hazmat sites and once on the map they are considered that to the EPA has confirmed that all contaminated soil & building materials have been removed and in a hazmat landfill -- you can only use a licensed contractor - it will big $$$$$$$ - property will be on top of the building & fire departments watch list