Reported by @philmassart (Mac OS 10.7 and 10.9):

[...] when checking the option "Show splashscreen", Frescobaldi doesn't show its window; I have to click on the Frescobaldi icon in the dock. I don't need to do that when the splashscreen doesn't show.

... by @PaulMorris (Mac OS 10.9):

I am also seeing the splash-screen-then-no-new-window-until-click-dock-icon behavior, [...]. I find that this problem doesn't occur if I uncheck "Show Splash Screen on Startup" in preferences, [...].

... and by three other users (Mac OS 10.9):

After the splash screen the application moves to the background. I have to click on the Frescobaldi icon in the dock to bring it to the front. Using [command]+[tab] to cycle through active applications doesn’t bring it to the front unless I’ve already clicked on the icon in the dock.

@philmassart: do you see this both in 10.9 and 10.7 or only on 10.9?
I suspect that the problem might be specific to 10.9.