Not bad, not great
The music in the game is decent. I won't discuss the jumping issue as it's been covered.
My main concern is the lack of a continue feature. I'm sure it was your original intention, so I guess that's more of my personal preference, but it sure was frustrating to make it to the second chapter only to quickly be taken out and have to restart. Also, the first boss fight starts rather abruptly. I literally had no time to dodge the samurai the first time I fought him. That aside, I like the idea, so kudos to you for making a completely off the wall game.