Here's two situations that could be deliberate decisions that seems as though they're broken:
This stands out whenever there are animations or transitions from one screen to another that usually are in a certain position, but every once in a while switch to a different layout for no apparent reason. This could be as simple as elements that are offset, or even elements that are clipped at the edge of the screen. The designer may even want the elements slightly clipped off the screen to de-emphasize them, but if this shows up only occasionally, there is a risk that it will seem broken. Overlapping elements are especially in danger of being misinterpreted.
Seemingly-Impossible Modes [with no clear entrance or exit]
Spotify comes to mind here, as I often notice it "freezing" on occasion between songs on my mobile phone. Noticeable things that make me think its broken are the lack of slider on the track-progress bar. What mode am I in? The screen shows a pause button, so clearly it thinks that it is playing, yet no music is audible and it shows no track-progress. How do I get my music?
In reality, this might be a design decision to show buffering, but it doesn't communicate to the user to wait a while. Worse yet, if the connection is quite bad, the buffering state of limbo might last a minute or two, with the user not realizing what is happening behind the scenes.