When I compile an Allegro windowed program with MingW32 and run, it first open a console window which says "1" then another which displays the program graphics.
How do I get rid of that console window?

Add -Wl,--subsystem,windows to the linker command line and you won't get unwanted console windows anymore.

whats wrong with -mwindows?

I've been told that -mwindows is outdated and may be removed in a future version of gcc and the -Wl,--subsystem,windows is now the prefered method.
Other than that, ther is nothing wrong with it.