What is the true definition of Home Park? If you look online multiple sources have it included the area around White Provisions that many people would refer to as "West Midtown" (
http://tiny.cc/1o2s1w). Assuming we're referring to the portion of Home Park between Northside and the Connector, between Atlantic Station and GT I think its safe to assume the trouble with the neighborhood is a few things. The most important is that it's pretty cut off from any other portions of the city. It's not very well connected to Atlantic Station nor does that portion of Georgia Tech's campus particular address 10th Street very well, so it acts as sort of a wall towards Home Park. Turner's campus, as well as some Georgia Tech facilities sort of separate it from Midtown across The Connector, but even then the portions of Midtown where 10th Street and 14th Street cross over don't really provide anything of interest. To the west, Northside Drive isn't a very pedestrian friendly road, effectively cutting off the neighborhood from the more trendy portion of Home Park or rather "West Midtown".
For the longest time the only food options were the fast food chains at the intersection of Hemphill, 14th, and Northside and while other stuff has moved in around the neighborhood, most of the nicer more attractive stuff has been occurring on the other side of Northside away from the more single family home portion of Home Park which as stated above isn't really super convenient if you're looking for a nice, walkable neighborhood.
I believe the neighborhoods location near GT has hurt as well as people who have owned the property in the area have utilized it all as primary rentals to college age kids. Because of its location they've never had issue renting the homes and units out to kids, so there was no reason to reinvest into their properties. This is why many of the properties are old and have hardly seen any renovations, this is also a reason why the neighborhood has been targeted by criminals - a lot of aloof college kids (many foreigners going to GT live in this neighborhood, based on my experiences there) who carry and have expensive electronics.
With that said, its only a matter of time before the neighborhood improves. There has been development along 14th Street with restaurants and other amenities, portions of Atlantic Station adjacent to the neighborhood are being (re)developed, and the area around White Provisions continues to explode. A lot of multifamily is being built in the area on the other side of Northside and all those under utilized lots between Howell / Northside & 14th and 8th Street will start to be redeveloped into residential or businesses to cater to the influx of new residents. Eventually the land in the more residential area of Home Park will become attractive enough for people to buy and redevelop and other areas, like 14th and Northside, should see redevelopment as the area becomes more attractive.