A few common items to be on the lookout for:  Look everywhere inside and out for peeling or missing paint and fix as necessary, test windows to make sure they open, can stay open, close, and lock (old wood windows may have problems doing this regularly or be stuck all together), review basement for any signs of standard black, non-toxic mold/standing water, make sure all stairs are cleared of tenant items (no bikes, boxes, etc.).   

I’m very interested in a multifamily property , and looking forward to partner up with someone from BiggerPockets to be my eyes and ears on site!

@Russ B.Changing of the locks can do wonders...

I don't have apartments (yet), but we do lock box showings all the time with our SFH's and plexes. 

You "simply" find a deal, lock it up, and then find a buyer.

Now, with that being said - you can still move to a less expensive/more affordable market and still invest out of state; don't think of yourself as locked into a state or area just because you live there.

You are letting someone speak in your ear without giving you the entire picture.

"We've locked ourselves out of the cabin and the combination isn't working!"  

For example, unless you buy a deal with some equity, your 10% to 25% equity downpayment is likely locked in the property for at least a few years.

Have a Realtor be the eyes, ears for you locally and have no problems telling you to walk from a property if it's not a good buy for you.