@Phineas Howie
Here in Pittsburgh, it depends. In 80% of single-family-home Zestimates, it's realistic to 10% of eventual buying costs about 60% of the time. However, when it's wrong the rest of the 40% of the time, we find it's as often wildly wrong as it is slightly wrong, that is, it is not slightly less accurate for the next 20%, and then just a bit less accurate for the next 10%, with 10% true outliers left over. No, it's within 10% of real sales price 60% of the time, and the other 40% it's inaccurate in a thoroughly unpredictable way. When it comes to multi-family investment properties, the Zestimate in the parts of Allegheny County that I've studied is less accurate than it is when it comes to single-family homes, to the tune of 50% on target within 10%, 50% inaccurate in the scattershot way I've described.
I would encourage you to think of the Zestimate as our outfit does, yet another tool in buying and selling properties, an independent statement of value that has outsized power over the decisions of casually-informed buyers and sellers, and even more importantly, a statement that can be manipulated to achieve your desired outcomes.
So my thinking goes like this: when YOU buy and sell as an investor, especially one making make-or-break first moves, you have to learn how to do your own comparative value assessments, and you have to learn how to do them using the same detailed techniques that the most experienced and successful local wholesalers and foreclosure buyers use, not agents who have the time to "pull comps" for free for every fresh-faced lookie-lookie with a preliminary loan approval letter in their pocket. To get within that hard 10% about 95% of the time, you also can't trust appraisers either hired by a bank or that you pay out of pocket.
This is how I do it for myself and how I back up my mentors in my own target area:
Physical inspections, county records, the MLS, Zillow.com, other real estate sites, accurate estimates of the true cost of repairs, all of these play a role. Your first step is Google Maps Street View. Your next step is a decent camera and YOUR OWN BOOTS on the ground. The next step is understanding the true cost of repairs in your target area, and that's a lot of work and knowledge. Then you have to master the local records system in that area. Then you study how the real estate websites, especially Zillow.com, handle sales pricing in the area. If you can, you make a contact with an agent who sets you up with access to the MLS in your target area. In Western Pennsylvania, there's a great computer system called "Matrix" that works with the West Penn Multi List. It can send you immediately email updates on every property listed for sale or reduced in price in a specific zip code. This is absolute gold for gaining the kind of in-depth sales knowledge of a target area I'm talking about.
If you want to really piss off a successful wholesaler at a foreclosure auction, ask her or him twice what he thinks the values of properties that are up for sale is, places that YOU haven't physically bothered to go to.