(I am now in a rush to test as many games as possible to help, so please do not mind the cursory reviewing style.)
MUSIC!! B)
I notice there are both mouse controls (where the direction is controlled by the mouse position) and keyboard controls (with the arrow keys, thank you for on behalf of my AZERTY!); I advise stating the controls somewhere, for example on the game page! You can still do it. :)
Playability is fine, including the smooth double jump.
The sounds are nice (sfxr? ;)), although I think a JUMP SOUND would have been great to add! And the "Mission complete!" voice sounded like it was straight out some anime (which was Mini Jam 114’s theme, but hey, the theme does not matter XD).
Nice idea to add variety (the rockets/missiles) once having collected some top secret notes! :) I just wish some more variety had continued to flow in; for example, you could have increased some parameter(s) (like scrolling speed, for instance) every time you get a "mission complete".
I liked the greyish colours, and the vanishing birds. :) Felt noir indeed; by the way, the cool music feels different, but it is so pleasant that I say it is no problem. X)
You wrote "maybe?" as for the use of the limitation, but I think you could argue that the platforms, birds, and rockets/missiles are temporary.
Played long enough to catch that the music does not loop! (At least on my system; I am using Firefox.)
Question on the thumbnail: who is the man on the right? A henchman, or the evil antagonist?
Takeaway: classic though immediately playable and pleasant. I think adding some more variety/progression over the course of the action would make the game more interesting in the long run, and maybe thinking of a clever contraint-related twist would be the icing on the cake. ;)
My fingers had a funny little time, I stopped at 8,332. :)