The quote above is from Activating an Item (DMG p. 141) and literally few rows below it there is an explicit explanation on how Consumables are items that need to activated.
“Consumables
Some items are used up when they are activated. A potion or an elixir must be swallowed, or an oil applied to the body. The writing vanishes from a scroll when it is read. Once used, a consumable item loses its magic.”
Well, my bad. That’s also stupid. So the only items you can use would be, like, whenever a GM says “You’d have to use an action to interact with that item!”
That blurb falls under magical items, specifically, so would non magical stuff still work? Poisons and Healers kits? If not then I guess the only use otherwise is environment interaction.
I really don’t know what it covers. Most of things that come to my mind would be considered as Free Actions anyways. Maybe one could trow a rock that has Light cast on it as “Use an Object” action if it wasn’t meant to hurt anyone? If the Fast Hands would be meant to be used more in non-combat situations it doesn’t really help to be able to do something as a Bonus Action instead of an Action.
Edit: After reading Fast Hands again I guess that the “Use an Object” is just a throw away part of it. Sleight of Hand as BA might be something that you would be able to use during combat. Would be pretty evil to snag the casting Focus from a caster so they wouldn’t be able to cast spells anymore. 
In real life people who can do sleight of hand really well can be rather scary good at it… I don’t see why that couldn’t be done in DnD.
Even the desingers get confused with this.
Sleight of hand, donning a shield and drawing a weapon, things like that. Only things that are specifically covered by the use an object rule, anything with special rules and effects is out. (Apart from the healing kit it seems, where they seem to have fucked up the wording.)
What a mess.
http://www.sageadvice.eu/2016/07/04/use-an-object-action/
Edit: The offical Sage Advice also states no magic items, but healer’s kits.
Well, at least the errata/clarification does follow suit with my poison application idea. That’s the main one I know of and do, though I guess I’ll have to correct the healing potion behavior (and just get the Healer feat if I want to fill that role).
It’s kind of funny because there’s this mixed message in how a Thief progresses. You’d think Fast Hands would lead into and combine with Use Magic Object when it comes to class features like most other Class Features do.