The graphics are nicely done despite being simple, and the music and sound effects fit the game quite neatly. I agree with NilaCk regarding the floaty jump and bullet speed, and prehaps some screenshake in places could help the game feel if not overdone.
I also felt that the rewind wasn't that useful. You said in an earlier comment that you didn't want to force it on people, but I feel thats not the correct approach. If a mechanic doesn't add to the game, it generally shouldn't be there in the first place. Thats not a hard and fast rule, but designing a core mechanic that people don't need to use is a little self defeating. I'd suggest reworking the mechanic a bit to tie it more into the gameplay and encourage its use.
But those bits aside, the game has a very fun base and is impressive for your first game. With some tweaking this could really be an excellent shooter.