I have this issue as well, and might have some possible suspicions about why it's happening. When I initially bought the first hobby "item" for the Internet hobby, I declined to place "it" and let it go into Storage. When I then wanted to place it later, due to the abysmal functions of finding something in Storage, I went to place it from the Buy Menu, aaaaaand... it said 0/1 on the hobby item. Digging through storage to try and find out if I had lost them somehow, no: turns out, computer, chair, and table are all separate items, and weren't counting for 1/1 on the Buy Menu. I did want to get 1/1, so I bought yet another one (set) from that menu, placed it, and after the fact, it said I had 2/1, which shouldn't have been possible.
The "new item" indicator, I suspect it has something to do with the fact that the items are a set, and only count together as a set, and you haven't been able to "see" all three of them yet unless you buy and place them. If that doesn't sort it out, then I'm not sure what else is necessary, but it's got to be something to do with this nature of them.
edit: Can confirm that buying the new "set" does away with the new item notification, even if viewing it initially in the Buy Menu does not.
