I just tried it on a different laptop without external monitors. The Browse dialog is completely on-screen. I am always working with external monitors so I don't know if I never tested that... Or, when something happens normally, it just doesn't mentally register?
That said, I do see an issue on the laptop with no monitor. The dialog opens to small to be useful. So, the first thing the user has to do is resize it an possibly move it. Also, the laptop I tested on is a newly issued laptop so I don't have any projects on it yet. Therefore, the dialog opened with centered at the SlickEdit Pro directory. Not sure what directory it would have gone to if a project was open.
Whenever possible, SE should try to predict the user's next need. That is, make the dialog big enough so that resize is not necessary, remember the last location the user placed the dialog (may they like it there), etc.....